
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
Evaluate \(\int_{0}^{1} P^{[2004]}(x) \, dx\) where \(P(x)=x^{3}-\frac{3}{2} x^{2}+x+\frac{1}{4}\), \(P^{[1]}(x)=P(x)\), and for \(n \geq 1\), \(P^{[n+1]}(x)=P^{[n]}(P(x))\).

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