
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 $AB = BC = CD = DE = EA = 3$ and $\angle ABC = \angle CDE = \angle
DEA = 90^\circ$. Moreover, the plane of triangle $ACD$ is parallel to $\overline{BE}$. Compute the area of triangle $BDE$.

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