
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
Given two particles moving at the same speed along the edges of equilateral $\triangle ABC$ in the direction $A \Rightarrow B \Rightarrow C \Rightarrow A$, where one starts at $A$ and the other at the midpoint of $\overline{BC}$, determine the ratio of the area enclosed by the path traced by the midpoint of the line segment joining the two particles to the area of $\triangle ABC$.

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