
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 with \( AB = BC = CD = DE = 3 \) and \( \angle ABC = \angle CDE = 60^\circ \). Additionally, the plane of triangle \( ABC \) is perpendicular to line \( \overline{DE} \). Determine the area of triangle \( BDE \).

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