
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 the function $f(x)$ is a decreasing function on $\mathbb{R}$ and its graph passes through points $A(-4, 1)$ and $B(0, -1)$, the inverse function of $f(x)$ is denoted as $f^{-1}(x)$. Find the value of $f^{-1}(1)$ and the solution set of the inequality $|f(x-2)| < 1$.

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