
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 $A=\{x \mid 3 \leq 3^x \leq 27\}$ and $B=\{x \mid \log_2{x} < 1\}$,

(1) Find the intersection $A \cap B$ and the union $A \cup B$.

(2) Given the set $C=\{x \mid 1 < x < a\}$. If $C \subseteq A$, find the range of the real number $a$.

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