
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 sets \( A = \{ x \mid -2 < x < -1, \text{ or } x > 1 \} \) and \( B = \{ x \mid x^2 + ax + b \leq 0, a, b \in \mathbb{R} \} \), if \( A \cup B = \{ x \mid x > -2 \} \) and \( A \cap B = \{ x \mid 1 < x \leq 3 \} \), find the values of \( a \) and \( b \).

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