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

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