
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 convex quadrilateral $EFGH$, we have $\angle E \cong \angle G$ and $\angle F \cong \angle H$, $EF = GH = 200$, and $EH \neq FG$. The perimeter of $EFGH$ is $720$. Find $\lfloor 1000 \cos E \rfloor.$

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