
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
There are 19 cards, each with a number written on it from $15, 16, 17, \ldots, 33$ respectively (one number per card). Vasya, Petya, and Misha, members of a math club, want to divide all these cards among themselves such that each person gets at least one card, and no one has a pair of cards where the difference between the numbers is odd. How many ways are there to divide the cards in this manner?

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