
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 $a > 0$, and define the sets $A = \{x \,|\, |x| \geq 2\}$ and $B = \{x \,|\, (x - 2a)(x + 3) < 0\}$.

(Ⅰ) When $a = 3$, find the set $A \cap B$;

(Ⅱ) If $A \cup B = \mathbb{R}$, find the range of the real number $a$.

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