
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
Let set $A=\{x \mid \frac{x+3}{x-1} \geq 0\}$, set $B=\{x \mid x^2-x-2 \leq 0\}$, and set $C=\{x \mid x \geq a^2-2\}$.  
(1) Find $A \cap B$.  
(2) If $B \cup C = C$, find the range of values for the real number $a$.

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