
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
 $ 30$  students participated in the mathematical Olympiad. Each of them was given  $ 8$  problems to solve. Jury estimated their work with the following rule:
1) Each problem was worth  $ k$  points, if it wasn't solved by exactly  $ k$  students;
2) Each student received the maximum possible points in each problem or got  $ 0$  in it;
Lasha got the least number of points. What's the maximal number of points he could have?  
Remark: 1) means that if the problem was solved by exactly  $ k$  students, than each of them got  $ 30 \minus{} k$  points in it.

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