
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 $y=f(x)$ is an even function on $R$ and for any $x∈R$, $f(x)=f(2-x)$. When $x∈[0,1]$, $f(x)=(x-1)^{2}$. The sum of all the zeros of the function $g(x)=f(x)- \log _{2017}|x-1|$ is $\_\_\_\_\_\_\_.$

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