
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
An equilateral triangle with side length $2$ has three smaller equilateral triangles constructed externally on each of its sides, each with side length $s$. If these three smaller triangles together cover an area exactly equal to half of the original triangle's area, what is the side length $s$ of these smaller triangles?
A) $\frac{1}{\sqrt{3}}$
B) $\frac{2}{\sqrt{3}}$
C) $\frac{1}{\sqrt{6}}$
D) $\sqrt{\frac{2}{3}}$
E) $\sqrt{\frac{3}{4}}$

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