
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 the vertices of a regular 300-gon, the numbers from 1 to 300 are arranged in some order, each number appearing exactly once. It turns out that for each number \(a\), there are as many numbers smaller than \(a\) among the 15 closest numbers to it clockwise as there are among the 15 closest numbers to it counterclockwise. A number that is larger than all 30 numbers closest to it is called "huge." What is the smallest possible number of huge numbers?

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