
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 pentagon $ABCDE$, side $\overline{AB}$ is extended past $B$ to $A'$ so that $A'B = AB$. Likewise, points $B'$, $C'$, $D'$, and $E'$ are constructed by extending $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, and $\overline{EA}$ such that $B'C = BC$, $C'D = CD$, $D'E = DE$, and $E'A = EA$ respectively. Now, suppose the points $A$, $B$, $C$, $D$, and $E$ are erased. Knowing only the locations of $A'$, $B'$, $C'$, $D'$, and $E'$, reconstruct the polygon $ABCDE$.

It is given that there exist real numbers $p$, $q$, $r$, $s$, and $t$ such that
\[
\overrightarrow{A} = p \overrightarrow{A'} + q \overrightarrow{B'} + r \overrightarrow{C'} + s \overrightarrow{D'} + t \overrightarrow{E'}.
\]

Find the ordered quintuple $(p,q,r,s,t)$.

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