
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 a regular tetrahedron \( A B C D \), points \( E \) and \( F \) are on edges \( A B \) and \( A C \) respectively, such that \( B E = 3 \), \( E F = 4 \), and \( E F \) is parallel to face \( B C D \). Find the area of \( \triangle D E F \).

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