
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]


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In an isosceles triangle, if perpendiculars are drawn from the intersection point of the angle bisectors to the sides, the three perpendiculars divide the triangle into two smaller and one larger kite (deltoid) shapes. For which isosceles triangle will the sum of the areas of the two smaller kites equal the area of the larger kite?

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