
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
Three equilateral triangles, each with side \(\sqrt{3}\), are arranged so they are all on the same side of a line containing one side of each vertex. Along this line, the midpoint of the base of one triangle serves as a vertex of the next triangle. Calculate the area of the region covered by the union of the three triangular regions.
A) \(\frac{9\sqrt{3}}{4}\)  
B) \(\frac{12\sqrt{3}}{8}\)  
C) \(\frac{15\sqrt{3}}{8}\)  
D) \(\frac{18\sqrt{3}}{8}\)  
E) \(\frac{21\sqrt{3}}{8}\)

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