
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 \( h(x) \) defined by 
\[
(x^{2^{2009} - 1} - 1)h(x) = (x+2)(x^2+1)(x^4+1)\cdots (x^{2^{2008}}+1) - 2
\]
Find \( h(3) \).

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