
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 by the equation \[(x^{2^{2009}-1}-1)f(x) = (x+1)(x^2+1)(x^4+1)\cdots (x^{2^{2008}}+1) - 1\]. Find $f(3)$.

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