
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
Vanya received three sets of candies for New Year. Each set contains three types of candies: hard candies, chocolates, and gummy candies. The total number of hard candies in all three sets is equal to the total number of chocolates in all three sets, and also to the total number of gummy candies in all three sets. In the first set, there are equal numbers of chocolates and gummy candies, and 7 more hard candies than chocolates. In the second set, there are equal numbers of hard candies and chocolates, and 15 fewer gummy candies than hard candies. How many candies are in the third set if it is known that there are no hard candies in it?

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