
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 isosceles paper triangle with sides of lengths $5, 5,$ and $6$ inches, is folded so that vertex $A$ (opposite the side of length $6$ inches) falls on the midpoint of side $BC$. Calculate the length in inches of the crease formed.
A) $\sqrt{32}$
B) $\sqrt{33}$
C) $\sqrt{34}$
D) $\sqrt{35}$
E) $\sqrt{36}$

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