
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 an even function $f(x)$ satisfies $f(x+1)=- \dfrac {1}{f(x)}$, and 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 \_\_\_\_\_.

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