
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
Let $A = \{x \mid x^2 - 2x - 3 > 0\}$, $B = \{x \mid -x^2 + 4x - 3 \geq 0\}$, and function $f(x) = x + 1$. If $x_0 \in A$ and $f[f(x_0)] \in A$, then the range of values of $x_0$ is ( ).

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