
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 for all $x \in \mathbb{R}$, $f(x) = f(2-x)$, and the equation $f(x) = 0$ has 5 distinct roots $x_i$ ($i=1,2,3,4,5$), then $x_1+x_2+x_3+x_4+x_5=$ ?

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