
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 $EFGH$, side $\overline{EF}$ is extended past $F$ to $E'$ such that $E'F = 2EF$. Points $F'$, $G'$, and $H'$ are similarly constructed using the same scaling factor of 2.

After this construction, points $E$, $F$, $G$, and $H$ are erased. You only know the locations of points $E'$, $F'$, $G'$, and $H'$, and want to reconstruct quadrilateral $EFGH$.

There exist real numbers $u$, $v$, $w$, and $x$ such that
\[
\overrightarrow{E} = u \overrightarrow{E'} + v \overrightarrow{F'} + w \overrightarrow{G'} + x \overrightarrow{H'}.
\]

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