
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
Let \[ P(x) = (3x^4 - 15x^3 + ax^2 + bx + c)(4x^3 - 36x^2 + dx + e) \], where \(a, b, c, d, e\) are real numbers. Suppose the set of complex roots of $P(x)$ includes $\{2, 3, 4, 5\}$ with at least one of the roots repeated. Find $P(7)$.

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