
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
Let $A = \mathbb{Q} \setminus \{0, 2\}$. Define a function $f : A \to \mathbb{R}$ such that for every $x \in A$, the following holds:
\[
f(x) + f\left(\frac{1}{1-x}\right) = \log|x|.
\]
Compute $f(2008)$. Enter your answer in the form "$\log(a)$", where $a$ is a specified number.

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