
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 a quadrilateral $WXYZ$, sides $WZ$, $XY$, $YZ$ are each 3 units. $\angle Y$ is a right angle, and $m\angle W = m\angle X = m\angle Z = 120^\circ$. Determine the length of segment $WX$, which can be expressed in simplest radical form as $p + q\sqrt{r}$ units, and find the value of $p+q+r$.

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