
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 $f(x) = |ax + 1|$ ($a \in \mathbb{R}$), the solution set of the inequality $f(x) \leq 3$ is $\{x | -2 \leq x \leq 1\}$.
1. Find the value of $a$;
2. If the function $g(x) = f(x) - |x + 1|$, find the minimum value of $g(x)$.

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