
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 a circle with radius $R$, a chord is drawn perpendicular to the diameter. The endpoints of this chord are connected to the endpoints of the diameter. Under what condition will the difference in the areas of the two triangles, having the chord as a common base, be maximal?

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