
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 $B := \mathbb{Q} \setminus \{0,1,2\}$ denote the set of all rationals other than 0, 1, and 2. A function $f : B \rightarrow \mathbb{R}$ has the property that for all $x \in B$,
\[
f\left( x\right) + f\left( 2 - \frac{1}{x}\right) = \log\lvert 2x\rvert.
\]
Compute the value of $f\left(\frac{1}{3}\right)$.

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