
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 with radius $500$ and height $150\sqrt{7}$. A bug starts at a point on the surface of the cone whose distance from the vertex of the cone is $100$, and crawls along the surface of the cone to a point on the exact opposite side whose distance from the vertex is $300\sqrt{2}$. Find the least distance that the bug could have crawled.

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