
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
In the coordinate plane, the curve \( xy = 2 \) intersects a circle at four points, three of which are \( (3, \frac{2}{3}), (-4, -\frac{1}{2}), \) and \( (\frac{1}{2}, 4) \). Find the fourth point of intersection.

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