
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 \( A = \left\{ x \mid x^{3} + 3x^{2} + 2x > 0 \right\} \) and \( B = \left\{ x \mid x^{2} + ax + b \leq 0 \right\} \), with \( A \cap B = \left\{ x \mid 0 < x \leq 2 \right\} \) and \( A \cup B = \left\{ x \mid x > -2 \right\} \), find the values of \( a \) and \( b \).

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