
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
A paper equilateral triangle with sides 6 inches each is folded so that one vertex falls exactly at the midpoint of the opposite side. What is the length of the crease?
A) $\frac{9\sqrt{3}}{2}$  
B) $\sqrt{3}$  
C) $\frac{3\sqrt{3}}{2}$  
D) $3$  
E) $\frac{5\sqrt{3}}{2}$

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