
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 $A=\left\{ x \mid x^2-3x < 0 \right\}$, $B=\left\{ x \mid (x+2)(4-x) \geqslant 0 \right\}$, and $C=\left\{ X \mid a < x \leqslant a+1 \right\}$.

(1) Find $A \cap B$;

(2) If $B \cup C = B$, find the range of values for the real number $a$.

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