
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
Let the universal set be $R$, and the sets $A=\{x|1<x<5\}$, $B=\{x|3\leq x\leq 6\}$. Find: (1) $A\cap B$  (2) $A\cup B$   (3) $C_{R}A\cap B$   (4) $C_{R}(A\cap B)$.

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