
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 $y=f(x)$ is a monotonically increasing function on its domain, its inverse function is $y=f^{-1}(x)$, and the graph of $y=f(x+1)$ passes through points A$(-4,0)$ and B$(2,3)$. If $|f^{-1}(x+1)|\leq 3$, then the range of $x$ is.

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