
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
Hexagon $ABCDEF$ is regular with side length 3. Set $T$ is made up of all line segments that have length 3 and whose endpoints are on adjacent sides of the hexagon. The midpoints of the line segments in set $T$ enclose a region. Find the area $A$ of this region.

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