
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
A total of  $n$  people compete in a mathematical match which contains  $15$  problems where  $n>12$ . For each problem,  $1$  point is given for a right answer and  $0$  is given for a wrong answer. Analysing each possible situation, we find that if the sum of points every group of  $12$  people get is no less than  $36$ , then there are at least  $3$  people that got the right answer of a certain problem, among the  $n$  people. Find the least possible  $n$ .

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