
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 $f(x)$ satisfies $f(x+1) = \frac{1}{f(x)}$, and $f(x)$ is an even function. When $x \in [0,1]$, $f(x) = x$. If in the interval $[-1,3]$, the function $g(x) = f(x) - kx - k$ has four zeros, then the range of the real number $k$ is _______.

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