
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
An equilateral triangle $ABC$ is inscribed in a circle, with side length $6$ cm. Another smaller equilateral triangle $DEF$ has its vertex $D$ on side $AB$ and the other two vertices $E, F$ on the circle. The distance from $D$ to vertex $A$ is $1$ cm. Find the area of triangle $DEF$.

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