
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 an equilateral triangle ABC, line segments are drawn from a point P to the vertices A, B, and C to form three identical triangles. The points D, E, and F are the midpoints of the three sides and they are joined as shown in the diagram. Determine the fraction of triangle ABC that is shaded.

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