
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
[asy] draw((-7,0)--(7,0),black+linewidth(.75)); draw((-3*sqrt(2),0)--(-2*sqrt(2),2)--(-sqrt(2),0)--(0,2)--(sqrt(2),0)--(2*sqrt(2),2)--(3*sqrt(2),0),black+linewidth(.75)); draw((-2*sqrt(2),0)--(-1*sqrt(2),2)--(0,0)--(sqrt(2),2)--(2*sqrt(2),0),black+linewidth(.75)); [/asy]
Six equilateral triangles, each with side length $2\sqrt{2}$, are arranged such that they all lie on the same side of a line containing one side of each vertex. Along this line, the base of one triangle shares its midpoint as a vertex with the next triangle. Compute the total area of the plane covered by the union of these six triangular regions.
A) $10\sqrt{3}$  
B) $9.5\sqrt{3}$  
C) $11\sqrt{3}$  
D) $12\sqrt{3}$  
E) $8.5\sqrt{3}$

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