
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 that function $f(x)$ is a monotonic function on $\mathbb{R}$, and ${f}^{-1}\left(x\right)$ is its inverse function, points $A(-1,3)$ and $B\left(1,1\right)$ are both on the graph of function $f\left(x\right)$. Determine the solution set for the inequality $\left|{f}^{-1}\left({2}^{x}\right)\right|<1$.

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