
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 inequality about $x$, $ax^2 + 3x + 2 > 0$ $(a \in \mathbb{R})$.

(1) Find the solution set when $a = -5$.

(2) Find the solution set of the inequality about $x$, $ax^2 + 3x + 2 > -ax - 1$ (where $a \in \mathbb{R}$).

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