
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 pentagon $ABCDE$, side $\overline{AB}$ is extended past $B$ to $A'$ so that $A'B = AB$. Similarly, extend $\overline{BC}$ to $B'$ so that $B'C = BC$, $\overline{CD}$ to $C'$ so that $C'D = CD$, $\overline{DE}$ to $D'$ so that $D'E = DE$, and $\overline{EA}$ to $E'$ so that $E'A = EA$. After this construction, points $A, B, C, D, E$ are erased. You know only the locations of points $A', B', C', D',$ and $E'$ and want to reconstruct pentagon $ABCDE$. There exist real numbers $p, q, r, s, t$ 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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