
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
Tanya and Vera are playing a game. Tanya has cards with numbers from 1 to 30. She arranges them in some order in a circle. For every two neighboring numbers, Vera calculates their difference by subtracting the smaller number from the larger one and writes down the resulting 30 numbers in her notebook. After that, Vera gives Tanya the number of candies equal to the smallest number written in the notebook. Tanya wants to arrange the cards to get as many candies as possible. What is the maximum number of candies Tanya can receive?

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