
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
Vika has 60 cards with numbers from 1 to 60. She wants to pair all the cards such that each pair has the same modulus of the difference between the numbers. How many ways are there to do this?

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