
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 \(B := \mathbb{Q} \setminus \{-1,2\}\) denote the set of all rationals other than \(-1\) and \(2\). Define a function \(f : B \rightarrow \mathbb{R}\) such that for all \(x \in B\),
\[
f(x) + f\left(2 - \frac{1}{x + 1}\right) = \log\lvert x + 1\rvert.
\]
Compute the value of \(f(2008)\). Enter your answer in the form "\(\log(a)\)", where \(a\) is some number.

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