
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
A deck of cards has 52 cards, with 13 cards each in the "Diamonds," "Clubs," "Hearts," and "Spades" suits. The cards are numbered as $2, 3, \cdots, 10, \mathrm{J}, \mathrm{Q}, \mathrm{K}, \mathrm{A}$. Two cards of the same suit with consecutive numbers are called a "straight flush," and $\mathrm{A}$ can be considered as 1 (i.e., $\mathrm{A}$ and 2 are consecutive). Determine the number of ways to draw 13 cards from this deck such that each rank appears exactly once, and no straight flush is formed.

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