
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
22. Given that the domain of function $f(x)$ is $(-2,2)$, and the function $g(x)=f(x-1)+f(3-2x)$. (1) Find the domain of function $g(x)$; (2) If $f(x)$ is an odd function and monotonically decreasing within its domain, find the solution set of the inequality $g(x)\leqslant 0$.

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