
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
Given that students earn 6 points for first place, 4 points for second, and 2 points for third place, and a bonus of 3 points is awarded to any student who finishes in each of the three different positions at least once, determine the minimum number of points a student must earn in the four races to guarantee earning more points than any other student.

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