
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 triangular prism $V-ABC$, the length of the lateral edge is 3 and the length of the base edge is 2. The section passing through the base edge $AB$ intersects the lateral edge $VC$ at point $D$. What is the minimum area of the section $\triangle ABD$?

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