
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 \( A = \{ x \mid (x-2)[x-(3a+1)] < 0 \} \) and \( B = \left\{ x \mid \frac{x-2a}{x-(a^2+1)} < 0 \right\} \),
1. Find \( A \cap B \) when \( a = 2 \).
2. Determine the range of real numbers \( a \) such that \( B \subseteq A \).

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