
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 a class of 60 students, each student's birthday is recorded as a specific month and date. Two questions are asked to each student: How many people in the class have the same birth month as you? How many people in the class have the same birth date as you (for example, January 12 and December 12 have the same date)? It was found that the answers to these questions included all integers from 0 to 14. What is the minimum number of students who share the same birthday in this class?

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