
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 right circular cone with a base radius of \(1 \, \text{cm}\) and a slant height of \(3 \, \text{cm}\), point \(P\) is on the circumference of the base. Determine the shortest distance from the vertex \(V\) of the cone to the shortest path from \(P\) back to \(P\).

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