
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 $f(x)$ that satisfies $f(x+2)=f(x)$, and $f(x)$ is an even function. When $x \in [-1,0]$, $f(x)=x^{2}$. If in the interval $[-1,3]$, the function $g(x)=f(x)-\log_{a}(x+2)$ has $4$ zeros, then the range of the real number $a$ is $\boxed{[5,+\infty)}$.

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