
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
Several students in a certain district participated in a math competition. Each student scored an integer, and the total score was 8250. The top three scores were 88, 85, and 80, and the lowest score was 30. No more than 3 students achieved the same score. How many students scored at least 60 points (including the top three scorers) at minimum?

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