Build a Side-by-Side Bilingual Question Paper

ROLE: Act as a bilingual assessment editor and print-layout planner.

CONTEXT: Create a mirrored paper from [SOURCE PAPER] in [LANGUAGE A] and [LANGUAGE B] using [LAYOUT CHOICE].

INPUTS — FILL EVERY PLACEHOLDER:
- [SOURCE PAPER]
- [LANGUAGE A]
- [LANGUAGE B]
- [LAYOUT CHOICE]
- [PAGE SIZE]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [OVERLEAF] Whitelist: https://www.overleaf.com/docs?encoded_snip={PERCENT_ENCODED_LATEX}. Overleaf requires a free account and sign-in before the imported project opens. Use pdflatex for the stated school-safe package set; use xelatex with fontspec only for multilingual documents. If the encoded URL exceeds 6,000 characters, output the full source plus manual paste steps instead of a broken link.
- [CODECOGS] Whitelist: https://latex.codecogs.com/png.image?{PERCENT_ENCODED_LATEX}. CodeCogs renders one equation image, not a document. Start permanent classroom PNGs with the encoded form of \dpi{150}, keep the URL short, and tell the teacher to download rather than hotlink it.

DO THIS:
1. Segment the source by question and subpart without changing order.
2. Translate each text segment while keeping formulas, placeholders, marks, numbering, and option labels fixed.
3. Pair each source segment with exactly one target segment.
4. Flag unavoidable length expansion before changing layout.
5. Generate fontspec-based XeLaTeX with a free Overleaf login note and fallback fonts rather than asserting font availability.
6. Provide a plain-text paired-line fallback if the encoded project link is too long.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Mirror a question containing the fraction 3/4 in two languages.
Expected result or check target: Both language lines show the same item number, marks, and 3/4 notation.
check this yourself
CHECK → https://latex.codecogs.com/png.image?%5Cfrac%7B3%7D%7B4%7D
(paste-fallback: \frac{3}{4})
Encoding note: The backslash and braces decode from %5C and %7B/%7D to the exact LaTeX fallback.

OUTPUT FORMAT:
1. Alignment Plan — chosen bilingual layout
2. Locked Structure — numbering, marks, options, and notation
3. Bilingual Paper — source and target paired item by item
4. Overflow Report — sections needing layout adjustment
5. Overleaf Package — XeLaTeX source and manual fallback

QUALITY AND TOOL GUARDRAILS:
- Preserve every placeholder, symbol, formula, mark value, question number, and option label exactly.
- Do not split a source item from its translation or silently renumber after a page break.
- Overleaf requires a free account; multilingual output must use XeLaTeX and fontspec with a tested fallback, not a promised installed font.
- CodeCogs is for single equations only and cannot render the bilingual paper.
- Do not translate proper nouns or technical terms when [TERMINOLOGY PREFERENCES] says to retain them.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.