
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
Given that the domain of function $f(x)$ is $(a,b)$, if the statement "$\exists x\_0 \in (a,b), f(x\_0) + f(-x\_0) \neq 0$" is false, then $f(a+b) =$ _____.

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