
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
Given quadrilateral $WXYZ$, side $\overline{WZ}$ is extended past $Z$ to $W'$ so that $W'Z = 2WZ$. Side $\overline{XY}$ is similarly extended past $Y$ to $X'$ so that $X'Y = 2XY$. However, side $\overline{WX}$ is extended past $X$ just to $Y'$ such that $Y'X = WX$. Side $\overline{YZ}$ is extended past $Z$ to $Z'$ such that $Z'Z = YZ$.

After this construction, points $W$, $X$, $Y$, and $Z$ are erased. You only know the locations of points $W'$, $X'$, $Y'$, and $Z'$ and want to reconstruct quadrilateral $WXYZ$.

There exist real numbers $a$, $b$, $c$, and $d$ such that
\[\overrightarrow{W} = a \overrightarrow{W'} + b \overrightarrow{X'} + c \overrightarrow{Y'} + d \overrightarrow{Z'}.\]
Enter the ordered quadruple $(a, b, c, d)$.

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