
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 a function $f(x)$ with a domain of $R$, satisfying $f(x) = f(2-x)$, and for any $1\leqslant x_{1} \lt x_{2}$, $\frac{{x_1}-{x_2}}{{f({x_1})-f({x_2})}} \gt 0$, then the solution set of the inequality $f(2x-1) - f(3-x) \geqslant 0$ is ____.

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