
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 the set \( A = \left\{(x, y) \left\lvert\, \frac{y-3}{x-1}=2\right., x, y \in \mathbf{R}\right\} \) and the set \( B = \{(x, y) \mid 4x + ay = 16, x, y \in \mathbf{R}\} \). If \( A \cap B = \varnothing \), then the value of the real number \( a \) is \(\quad\) .

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