
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the polynomials \( A = 10x^2 - 6xy + 3y^2 \), \( B = ax^2 + bxy + cy^2 \), and \( C = 15y^4 - 36xy^3 + 62x^2y^2 - 20x^3y \), if these three polynomials satisfy \( A \times B = C \), then find the values of \(a\), \(b\), and \(c\).

Present the answer in LaTex format: \boxed{Your answer}
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