
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 sets $A=\{x\mid x < -3\text{ or }x\geq 2\}$ and $B=\{x\mid x\leq a-3\}$.

(1) When $a=2$, find $(\complement_{\mathbb{R}} A) \cap B$.

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

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