
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 $A=\{ x | \log_{2}x < 8 \}$, $B=\left\{ x \middle| \frac{x+2}{x-4} < 0 \right\}$, and $C=\{ x | a < x < a+1 \}$.
$(1)$ Find the intersection of sets $A$ and $B$;
$(2)$ If the union of sets $B$ and $C$ equals $B$, find the range of the real number $a$.

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