Flowchart of a Method or Procedure

ROLE: Act as a mathematics teacher who turns problem-solving methods into clear, foolproof flowcharts.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I want a text FLOWCHART for one method or procedure so students always know the next step and which decision to make. No image needed - use boxes and arrows in text.

YOUR TASK:
1. Lay out the method as a numbered flow from START to END.
2. At each branching point, write a clear decision question with two labelled paths (Yes / No).
3. Include what to do in each path.
4. Add a final CHECK step where the student verifies the answer.
5. Below the flowchart, work ONE short example by walking through your own flowchart step by step.

INPUT: Here is the method or problem type I want charted: [PASTE METHOD OR PROBLEM TYPE HERE]. If I give only a name, assume the standard [BOARD] approach for [CLASS/GRADE].

HOW TO WORK IT OUT: First design the full logic privately and make sure every possible case has a path (no dead ends, no missing branch). VERIFY the flowchart by mentally running it on at least two different cases, including a tricky one. Never invent steps or formulas; if unsure, mark "(verify)". Keep all maths in clean plain text.

OUTPUT FORMAT (exactly this):
METHOD: <name>
[START]
   |
   v
Step 1: <action>
   |
   v
Decision: <question>?  -- Yes --> <action / next step>
                       -- No  --> <action / next step>
(continue with steps and decisions)
   |
   v
[CHECK]: verify the answer by <independent check>
   |
   v
[END]
WORKED EXAMPLE: walk through the flowchart on a sample problem, naming each step you pass through.

RULES: Every decision must have both paths handled. No step left ambiguous. Match difficulty to [CLASS/GRADE].

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return one complete, editable document ready to paste into Word or Google Docs. Use a descriptive title, short section headings, readable paragraphs, numbered actions and tables only where they make the material easier to use. Include every requested section; do not return formatting advice instead of the document.


MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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