
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 class has 25 students. The teacher wants to prepare $N$ candies for a competition and distribute them according to scores (students with the same score get the same number of candies, and those with lower scores get fewer candies, which can be 0). What is the minimum value of $N$ that allows such distribution, regardless of how many questions there are in the competition or how the students perform?

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