
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 with sides of length 1 are shown shaded in a larger equilateral triangle. The total shaded area is half the area of the larger triangle. What is the side-length of the larger equilateral triangle?
A) \(\sqrt{5}\)
B) \(\sqrt{6}\)
C) \(\frac{5}{2}\)
D) \(\frac{3\sqrt{3}}{2}\)
E) \(1 + \sqrt{3}\)

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