
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 an increasing function on \( \mathbf{R} \), and its graph passes through the points \( A(0,-2) \) and \( B(3,2) \), determine the solution set of the inequality \( |f(x+1)| \geq 2 \).

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