
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 set $A = \{ x \mid a - 2 \leq x \leq 2a + 3, x \in \mathbb{R}\}$, $B = \{ x \mid x^2 - 6x + 5 \leq 0\}$.  
(1) If $A \cap B = B$, find the range of real number $a$;  
(2) If $A \cap \overline{B} = \emptyset$, find the range of real number $a$.

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