
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 theater troupe, there are 60 actors. Every pair of actors has performed in at least one play together. In each play, no more than 30 actors are involved.

What is the minimum number of plays the theater could have produced?

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