
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 the function $f(x) = |x-1| + |x+a|$, and $g(x) = \frac{1}{2}x + 3$,

(1) When $a = -2$, find the solution set of the inequality $f(x) < g(x)$;

(2) If $a > -1$, and when $x \in [-a, 1]$, the inequality $f(x) \leq g(x)$ has a solution, find the range of the real number $a$.

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