
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 stock  $N$  candies, hold the Olympics and give away all  $N$  candies for success in it (those who solve equally tasks should get equally, those who solve less  get less, including, possibly, zero candies). At what smallest  $N$  this will be possible, regardless of the number of tasks on Olympiad and the student successes?

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