
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
There are 25 students in a class. The teacher wants to stockpile $N$ candies, conduct a competition, and distribute all $N$ candies based on the students' performance (students who solved the same number of problems should receive the same number of candies, students who solved fewer problems should receive fewer candies, including possibly zero candies). What is the minimum $N$ for which this will be possible regardless of the number of problems in the competition and the students' success?

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