
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 \( 500 \) and a height of \( 300 \). A bug starts at a point on the surface of the cone whose distance from the vertex is \( 150 \), and crawls along the surface to a point on the exact opposite side of the cone whose distance from the vertex is \( 450 \). What is the shortest distance the bug could have crawled?

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