
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
A right circular cone has a base radius of $700$ units and a slant height of $250\sqrt{3}$. A butterfly starts at a point on the surface of the cone, $150$ units from the vertex, and crawls to a point directly opposite of the cone, $400$ units from the vertex. Find the least distance that the butterfly could have crawled.

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