
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
Determine the value of $g(-1)$ for the function $f(x)$ defined by the equation:
\[
(x^{2^{2007}+1} - 1)f(x) = (x-1)(x^2-1)(x^8-1)\cdots (x^{2^{2006}}-1) - 1
\]

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