
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
Given a regular triangular pyramid \( V-ABC \) with base side length 4 and lateral edge length 8. A plane passes through point \( A \) and intersects the lateral edges \( VB \) and \( VC \) at points \( E \) and \( D \), respectively. Find the minimum perimeter of the cross-sectional triangle \( \triangle AED \).

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