
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 sets $A=\left\{x \mid 3 < 3^{x} < 9 \right\}$, $B=\left\{x \mid 1 < \log_{2}x < 4 \right\}$, $C=(a,a+3)$.  
$(1)$ Find $(C_{R}A) \cap B$;  

$(2)$ If $A \subseteq C$, find the range of the real number $a$.

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