
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 $A=\left\{x|x < -2\text{ or }3 < x < 4\right\},B=\left\{x|{x}^{2}-2x-15\leqslant 0\right\}$. Find:

$(1)A\cap B$;

$(2)$ If $C=\left\{x|x\geqslant a\right\}$, and $B\cap C=B$, find the range of $a$.

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