
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 $A'$ such that $A'B = AB$. Points $B'$, $C'$, $D'$, and $E'$ are similarly constructed for the remaining sides of the pentagon.

After this construction, the original points $A$, $B$, $C$, $D$, and $E$ are erased. You know only the locations of points $A'$, $B'$, $C'$, $D'$, and $E'$ and need to reconstruct pentagon $ABCDE$.

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

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