
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 \( A := \mathbb{Q} \backslash \{0, 1\} \) denote the set of all rationals other than 0 and 1. A function \( f: A \rightarrow \mathbb{R} \) has the property that for all \( x \in A \),
\[ f(x) + f\left(1 - \frac{1}{x}\right) = \log |x| . \]

Compute the value of \( f(2007) \).

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