
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
The diagram shows two equilateral triangles. The distance from each point of the smaller triangle to the nearest point of the larger triangle is $\sqrt{3}$. What is the difference between the lengths of the edges of the two triangles?

A) $2 \sqrt{3}$  
B) $4 \frac{1}{2}$  
C) $3 \sqrt{3}$  
D) 6  
E) $4 \sqrt{3}$

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