
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
Two particles move along the edges of a square $\square ABCD$ in the direction $A \Rightarrow B \Rightarrow C \Rightarrow D \Rightarrow A$, starting simultaneously and moving at the same speed. One starts at $A$, and the other starts at the midpoint of $\overline{AB}$. Find the ratio of the area of the region $R$ to the area of $\square ABCD$.

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