
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 two cubic polynomials $P(x)$ and $Q(x)$ where $P(x) = x^3 + 3x^2 - 3x - 9$, construct $Q(x)$ by replacing each nonzero coefficient of $P(x)$ with their arithmetic mean. Determine the value of $Q(1)$.

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