
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 $ABCD$ in a plane, we extend side $\overline{AB}$ past $B$ to a point $A'$ such that $A'B = rAB$. Similarly, points $B',$ $C',$ and $D'$ are constructed such that $B'C = rBC$, $C'D = rCD$, and $D'A = rDA$. If points $A, B, C,$ and $D$ are erased, you know only $A'$, $B'$, $C'$, and $D'$ and must reconstruct the quadrilateral $ABCD$.

It is known that there are real numbers $p, q, r, s$ such that:
\[
\overrightarrow{A} = p \overrightarrow{A'} + q \overrightarrow{B'} + r \overrightarrow{C'} + s \overrightarrow{D'}.
\]
Determine the ordered quadruple $(p, q, r, s)$ when $r = 2$.

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