
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 \[ P(x) = (3x^4 - 33x^3 + px^2 + qx + r)(4x^4 - 100x^3 + sx^2 + tx + u), \] where $p, q, r, s, t, u$ are real numbers. Suppose that the set of all complex roots of $P(x)$ is $\{2, 3, 4, 6, 7\}.$ Find $P(8).$

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