
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 mathematical olympiad students received marks for any of the four areas: algebra, geometry, number theory and combinatorics. Any two of the students have distinct marks for all four areas. A group of students is called *nice* if all students in the group can be ordered in increasing order simultaneously of at least two of the four areas. Find the least positive integer N, such that among any N students there exist a *nice* group of ten students.

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