
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 a rectangle $XYZW$ in the plane with side lengths $XY = 2$ and $YZ = 1$. Let $P$ be a point in the same plane, and let the distances from $P$ to $X$, $Y$, and $Z$ be $u, v,$ and $w$ respectively. If $u^2 + w^2 = v^2$, what is the greatest distance that $P$ can be from $W$?
A) 0
B) 1
C) $\sqrt{2}$
D) 2
E) 1 + $\sqrt{2}$

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