
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
We draw a chord from a point on the plane of a given circle to the circle. In which position of the chord will the area of the triangle, whose one vertex is the center of the circle and whose other two vertices are defined by the intersection points of the chord with the circle, be maximum? Construct this chord.

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