
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 \[P(x) = (3x^5 - 45x^4 + ax^3 + bx^2 + cx + d)(4x^5 - 100x^4 + ex^3 + fx^2 + gx + h),\] where $a, b, c, d, e, f, g, h$ are real numbers. Suppose that the set of all complex roots of $P(x)$ is $\{1, 2, 2, 3, 4, 4, 5, 5, 5\}.$ Find $P(7).$

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