
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 a quadrilateral $PQRS,$ side $\overline{PQ}$ is extended past $Q$ to $P'$ so that $P'Q = PQ.$ Points $Q'$, $R'$, and $S'$ are similarly constructed.

After this construction, points $P,$ $Q,$ $R,$ and $S$ are erased. You only know the locations of points $P',$ $Q',$ $R'$ and $S',$ and want to reconstruct quadrilateral $PQRS.$

There exist real numbers $u,$ $v,$ $w,$ and $x$ such that
\[\overrightarrow{P} = u \overrightarrow{P'} + v \overrightarrow{Q'} + w \overrightarrow{R'} + x \overrightarrow{S'}.\]
Find the ordered quadruple $(u,v,w,x).$

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