
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 \( A \), \( B \), \( C \), and \( D \) are located in 3-dimensional space with \( AB = BC = CD = DA = 2 \) and \( \angle ABC = \angle BCD = 120^\circ \). The plane of triangle \( ABC \) is parallel to the line \( \overline{AD} \). Calculate the area of triangle \( BCD \).

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