
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 function $f(x)=\sqrt{-{x^2}+5x-6}$ with domain $A$, and the set $B=\{x||2^{x}-9|\leqslant 7\}$, where the universal set is the set of real numbers $R$.  
$(1)$ Find the sets $A$ and $B$;  
$(2)$ Find the sets $A\cap B$ and $\complement _{R}B$.

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