
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 circle $W$, diameters $EF$ and $GH$ are perpendicular to each other intersecting at the center $O$. Point $P$ is located on the extension of $EW$ such that $P$ is outside of circle $W$ and $WP = WO$. Calculate the ratio of the length of $PE$ to the length of $WO$ if $\measuredangle WPG = 90^\circ$.
A) 1
B) $\sqrt{2}$
C) $\sqrt{3}$
D) 2
E) $\frac{2\sqrt{3}}{3}$

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