
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
The organizers of a mathematics competition decided to take pictures of 60 participants. It is known that no more than 30 participants can fit in one picture, but any two students must appear in at least one picture together. What is the minimum number of pictures needed to achieve this?

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