
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 set $A=\{1,2,3\}$, and the set $B=\{x|a+1 < x < 6a-1\}$, where $a\in R$.
(1) Write out all the proper subsets of set $A$;
(2) If $A\cap B=\{3\}$, find the range of $a$.

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