
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
Consider the function \(f(x)\) defined as
\[
(x^{3^{2008}-1}-1)f(x) = (x+1)(x^3+1)(x^9+1)\cdots (x^{3^{2007}}+1) + (x^2-1) - 1
\]
Find \(f(3)\).

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