
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 function $f(x+1)$ is an odd function defined on $\mathbb{R}$, if for any given unequal real numbers $x_{1}, x_{2}$, the inequality $x_{1}f(x_{1})+x_{2}f(x_{2}) > x_{1}f(x_{2})+x_{2}f(x_{1})$ always holds, determine the solution set of the inequality $f(2-x) < 0$.

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