
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 $EFGH$, extend each side by a different factor: $\overline{EF}$ past $F$ to $E'$ such that $E'F = 3EF$, $\overline{FG}$ past $G$ to $F'$ such that $F'G = 2FG$, $\overline{GH}$ past $H$ to $G'$ such that $G'H = 3GH$, and $\overline{HE}$ past $E$ to $H'$ such that $H'E = 2HE$. After extending these points, $E,$ $F,$ $G,$ and $H$ are erased. Determine the original quadrilateral's vertices $EFGH$ in terms of the new points $E',$ $F',$ $G',$ and $H'$.

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