
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 game "Sportloto-Shish," the main prize draw follows these rules. Each participant in the studio independently writes any number of different pairs of distinct integers from the set {1, 2, 3, 4, 5}. If any of the pairs written by some participants coincide, those participants share the main prize. How many participants must be in the studio to ensure that the prize is definitely awarded?

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