
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 $y=f(x)$ with a period of $2$, and when $x \in [0,2]$, $f(x)=(x-1)^{2}$, if $g(x)=f(x)-\log_{5}|x-1|$, then the sum of all zeros of the function $y=g(x)$ is ______.

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