
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
Through the midpoints of two sides of a triangle \(ABC\), we draw the medians and connect the points that trisect the third side with the opposite vertex. Thus, inside, we obtain a bowtie shape (two triangles joined by a vertex). It is required to calculate the fraction of the total surface area of the triangle that the bowtie shape represents.

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