
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
Let the set $A = \{x | (x+1)(4-x) \leq 0\}, B = \{x | 2a \leq x \leq a+2\}$.

(1) If $A \cap B \neq \emptyset$, find the range of the real number $a$.

(2) If $A \cap B = B$, find the range of the real number $a$.

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