
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
In square $EFGH$, points $M$ and $N$ lie on $\overline{EH}$ and $\overline{EF}$ respectively. Segments $\overline{FM}$ and $\overline{GN}$ intersect at right angles at $O$, where $FO = 8$ and $MO = 9$. Determine the length of the diagonal of square $EFGH$.
A) $17\sqrt{2}$
B) $34\sqrt{2}$
C) $32\sqrt{2}$
D) $64\sqrt{2}$
E) $81\sqrt{2}$

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