
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 $M=\{x|x^{2}-3x-18\leqslant 0\}$, $N=\{x|1-a\leqslant x\leqslant 2a+1\}$.
$(1)$ If $a=3$, find $M\cap N$ and $\complement_{\mathbb{R}}N$;
$(2)$ If $M\cap N=N$, find the range of the real number $a$.

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