
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 $A=\left\{x \middle| \frac{x-3}{x-7} < 0 \right\}$, $B=\left\{x \middle| x^2 - 12x + 20 < 0 \right\}$, $C=\left\{x \middle| 5-a < x < a \right\}$,  
(1) Find $A \cup B$, $(\complement_{\mathbb{R}} A) \cap B$;  
(2) If $C \subseteq (A \cup B)$, find the range of the real number $a$.

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