
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
For $\forall x\in R$, if the function $f\left(x\right)$ satisfies $f\left(x\right)+f\left(2-x\right)=0$, then $f\left(x\right)=$____. (There may be multiple answers, write down one of them).

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