
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
Given an isosceles right triangle $ABC$ where $AB = AC = 10$, a rectangle $EFGH$ is constructed inside it such that vertices $E$ and $F$ lie on $AB$, vertex $G$ lies on $BC$, vertex $H$ lies on $AC$. If $EG = 6$ and $EH = 8$, determine the length of diagonal $EF$ of the rectangle $EFGH$.
A) 8
B) 9
C) 10
D) 11

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