
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 \[P(x) = (x^5 - 15x^4 + ax^3 + bx^2 + cx + d)(2x^6 - 42x^5 + ex^4 + fx^3 + gx^2 + hx + i),\] where \(a, b, c, d, e, f, g, h, i\) are real numbers. Suppose that the set of all complex roots of \(P(x)\) is \(\{1, 2, 3, 4, 5, 6\}.\) Find \(P(7).\)

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