
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 sets $M=\{x| -2 \leq x \leq 5\}$, $N=\{x| a+1 \leq x \leq 2a-1\}$.  
$(1)$ When $a=2$, find $M \cap N$ and $M \cup N$;  
$(2)$ If $M \supseteq N$, find the range of real number $a$.

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