
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 side length $3$, are arranged in a row, each following triangle's base vertex starting from the midpoint of the base of the previous triangle. They are all oriented such that they lie on the same side of the horizontal line. Calculate the area of the region of the plane that is covered by the union of the six triangular regions.
A) $9\sqrt{3}$
B) $12\sqrt{3}$
C) $10.6875\sqrt{3}$
D) $15\sqrt{3}$

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