
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 $ABCD$, each side $\overline{AB}, \overline{BC}, \overline{CD}, \overline{DA}$ is extended past $A, B, C, D$ respectively to $A'', B'', C'', D''$ such that $AA'' = 2AB, BB'' = 3BC, CC'' = 2CD, DD'' = 2DA$. After extending, the original points $A, B, C, D$ are erased. You only know the locations of points $A'', B'', C'', D''$. Reconstruct the quadrilateral $ABCD$.

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