
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 decreasing function $f(x)$ defined on $\mathbb{R}$ whose graph passes through points $A(-2, 2)$ and $B(2, -2)$, if the inverse function of $f(x)$ is $f^{-1}(x)$, then the solution set of the inequality $|f^{-1}(x+1)| \leq 2$ is.

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