
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 the sets \( A = \left\{ (x, y) \mid \frac{y - 3}{x - 2} = a + 1 \right\} \) and \( B = \left\{ (x, y) \mid (a^2 - 1)x + (a - 1)y = 15 \right\} \), if \( A \cap B = \varnothing \), find the value of the real number \( a \).

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