
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
Trapezoid $EFGH$ has $\overline{EF}\parallel\overline{GH}$, with $EF=2 \times GH$. The sides $FG=GH=37$, and $\overline{EH}\perp\overline{FH}$. Let $Q$ be the intersection of the diagonals $\overline{EG}$ and $\overline{FH}$, and let $R$ be the midpoint of $\overline{FH}$. Given that $QR=17$, the length of $EH$ can be written in the form $a \sqrt{b}$, where $a$ and $b$ are positive integers, and $b$ is not divisible by the square of any prime. Determine $a+b$.
A) 32
B) 34
C) 35
D) 36

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