
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
Nick and Tim play a game where each round cannot end in a draw. In a round, the losing player must take at least one candy, and the winning player takes a few more candies than the loser. They have pre-determined the number of candies the loser and winner each take per round (two given positive integers). After a certain number of rounds, Nick has a total of 30 candies, Tim has a total of 25 candies, and it is known that Tim won a total of 2 rounds. The question is: how many candies should the winner take in each round?

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