
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 the function $f(x)$ defined on $\mathbb{R}$ satisfies $f(x)=-f(2-x)$, and $f(x)$ is increasing when $x < 1$. If $x_{1}+x_{2} > 2$ and $(x_{1}-1)(x_{2}-1) < 0$, calculate the value of $f(x_{1})+f(x_{2})$.

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