
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
Solve the following problems:  
$(1)$ Let $S=\{x|x \lt -1$ or $x \gt 5\}$, $T=\{x|a \lt x \lt a+8\}$, $S$⋃$T=R$, find the range of $a$;  
$(2)$ If $S=\{x|-2\leqslant x \lt 5\}$, $T=\{x|a+1\leqslant x\leqslant 2a-1\}$, and $S$⋂$T=T$, find the range of real number $a$.

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