
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
Points \(A, B, C, D,\) and \(E\) are located in 3-dimensional space where \(AB = BC = CD = DE = EA = 3\) and \(\angle ABC = \angle CDE = \angle DEA = 120^\circ\). The plane of triangle \(ABC\) is parallel to \(\overline{DE}\). Determine the area of triangle \(BDE\).

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