
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 $M=\{x|-2\leqslant x\leqslant 5\}$, $N=\{x|a+1\leqslant x\leqslant 2a-1\}$,  
$(1)$ If $a= \frac {7}{2}$, find $M\cup N$; $(\complement_{\mathbb{R}}M)\cap N$;  
$(2)$ If $M\supseteq N$, find the range of the real number $a$.

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