
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 \( B := \mathbb{Q} \setminus \{-1, 0, 2\} \) denote the set of all rationals other than -1, 0, and 2. A function \( f : B \rightarrow \mathbb{R} \) has the property that for all \( x \in B \),
\[
f\left( x \right) + f\left( 2 - \frac{1}{x} \right) = \log |2x|.
\]
Compute the value of \( f(2012) \).

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