
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 $f(x) = |x + a| + |x + 3|$, $g(x) = |x - 1| + 2$.

(1) Solve the inequality $|g(x)| < 3$;  
(2) If for any $x_1 \in \mathbb{R}$, there exists $x_2 \in \mathbb{R}$ such that $f(x_1) = g(x_2)$ holds, find the range of the real number $a$.

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