
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 $f(x) = |x-1| + |x+2|$.
1. Solve the inequality $f(x) \geq 5$;
2. If the inequality $f(x) > a^2 - 2a - 5$ holds for any $x \in \mathbb{R}$, find the range of $a$.

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