
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
The hypotenuse of a right triangle is equal to \( c \). The projection of the vertex of the right angle onto the hypotenuse divides it into two segments, the smaller of which relates to the larger as the larger relates to the entire hypotenuse. Determine the area of the triangle.

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