
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
Consider an equilateral triangle where all sides measure 6 inches. The triangle is folded so that vertex $A$ exactly aligns with the midpoint of side $BC$. Determine the length in inches of the crease formed by this fold.
A) $3\sqrt{3}$
B) $3\sqrt{2}$
C) $4\sqrt{3}$
D) $2\sqrt{3}$
E) $5\sqrt{3}$

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