
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
Find the minimum length of segment \( AB \), if point \( A \) belongs to the set defined by the equation \( y^{2} - 9 + 2 y x - 12 x - 3 x^{2} = 0 \), and point \( B \) belongs to the set defined by the equation \( y^{2} + 3 - 4 x - 2 y + x^{2} = 0 \).

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