
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 the cyclic quadrilateral $EFGH$ where the side lengths are distinct integers all less than $20$ such that $EG \cdot GH = EF \cdot FH$. What is the largest possible value of $EH$?
A) $\sqrt{375}$  
B) $\sqrt{394}$  
C) $\sqrt{400}$  
D) $\sqrt{405}$

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