
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
In square $EFGH$ with side length $40$, point $Q$ lies inside such that $EQ = 16$ and $FQ = 34$. The centroids of $\triangle{EFQ}$, $\triangle{FgQ}$, $\triangle{GHQ}$, and $\triangle{HEQ}$ are vertices of a new convex quadrilateral. What is the area of this quadrilateral?

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