
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 $A = \{x \mid x^2+x-2 \leq 0\}$ and $B = \{x \mid 2 < x+1 \leq 4\}$, let set $C = \{x \mid x^2+bx+c > 0\}$ such that $(A \cup B) \cap C = \emptyset$ and $(A \cup B) \cup C = \mathbb{R}$. Find the values of the real numbers $b$ and $c$.

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