
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 universal set $U = \mathbb{R}$, $A = \{x | x^{2}-x-6 \leqslant 0\}$, $B = \{x | \frac{1}{2} \leq 2^x \leq 16\}$, $C = \{x | m-1 < x < m+1\}$.  
$(1)$ Find $A \cap B$;  
$(2)$ If $C \subseteq \complement_{U}(A \cap B)$, find the range of real number $m$.

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