
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 $A := \mathbb{Q} \setminus \{0,-1\}$ denote the set of all rationals other than 0 and -1. Define a function $f : A \rightarrow \mathbb{R}$ such that for all $x \in A$,
\[
f\left( x\right) + f\left( 1 + \frac{1}{x}\right) = \log\lvert x\rvert.
\]
Compute the value of $f(2023)$.

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