
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
Let $ABCDEF$ be a regular hexagon. Let $G, H, I, J, K,$ and $L$ be the centers, respectively, of equilateral triangles with bases $\overline{AB}, \overline{BC}, \overline{CD}, \overline{DE}, \overline{EF},$ and $\overline{FA},$ each exterior to the hexagon. What is the ratio of the area of hexagon $GHIJKL$ to the area of hexagon $ABCDEF$?
A) $\frac{7}{6}$
B) $\sqrt{3}$
C) $2\sqrt{3}$
D) $\frac{10}{3}$
E) $\sqrt{2}$

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