
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
A rhombus with side length \( a \) and an acute angle of \( 60^\circ \) has an inscribed circle. Determine the area of the quadrilateral whose vertices are the points of tangency of the circle with the sides of the rhombus.

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