
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 $A'B = AB.$ Similarly, points $B',$ $C',$ $D',$ and $E'$ are constructed by extending $\overline{BC},$ $\overline{CD},$ $\overline{DE},$ and $\overline{EA}$ respectively, such that $B'C = BC,$ $C'D = CD,$ $D'E = DE,$ and $E'A = EA.$ After this construction, points $A,$ $B,$ $C,$ $D,$ and $E$ are erased. You only know the locations of points $A',$ $B',$ $C',$ $D',$ and $E',$ and want to reconstruct pentagon $ABCDE.$

There exist real numbers $p,$ $q,$ $r,$ $s,$ and $t$ such that
\[
\overrightarrow{A} = p \overrightarrow{A'} + q \overrightarrow{B'} + r \overrightarrow{C'} + s \overrightarrow{D'} + t \overrightarrow{E'}.
\]
Enter the ordered quintuple $(p,q,r,s,t).$

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