
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
Six equilateral triangles, each with a side length of 3 units, are arranged sequentially along a straight line, with each triangle sharing a vertex with the next. The midpoint of the base of one triangle is a vertex of the next, similar to the original setup. Calculate the area of the region covered by the union of these six triangular regions.
A) $10\sqrt{3}$
B) $11\sqrt{3}$
C) $10.6875\sqrt{3}$
D) $12\sqrt{3}$
E) $13.5\sqrt{3}$

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