
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
Let $P_1 P_2 P_3 P_4 P_5 P_6$ be a regular hexagon with edge-centered distance (distance from the center to the midpoint of a side) of 2. If $Q_i$ is the midpoint of the side $P_i P_{i+1}$ for $i=1,2,3,4$, calculate the area of quadrilateral $Q_1 Q_2 Q_3 Q_4$.

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