
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
Find all functions  $f$  that is defined on all reals but  $\tfrac13$  and  $- \tfrac13$  and satisfies \[ f \left(\frac{x+1}{1-3x} \right) + f(x) = x \] for all  $x \in \mathbb{R} \setminus \{ \pm \tfrac13 \}$ .

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