
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 $A=\left\{ x \mid \frac{1-x}{x-7} > 0 \right\}$ and $B=\{x \mid x^{2}-2x-a^{2}-2a < 0\}$.

(1) When $a=4$, find the intersection $A\cap B$.

(2) If $A\subseteq B$, determine the range of real numbers $a$.

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