
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 is a standard deck of  $52$  cards without jokers. The deck consists of four suits(diamond, club, heart, spade) which include thirteen cards in each. For each suit, all thirteen cards are ranked from “ $2$ ” to “ $A$ ” (i.e.  $2, 3,\ldots , Q, K, A$ ). A pair of cards is called a “*straight flush*” if these two cards belong to the same suit and their ranks are adjacent. Additionally, " $A$ " and " $2$ " are considered to be adjacent (i.e. "A" is also considered as " $1$ "). For example, spade  $A$  and spade  $2$  form a “*straight flush*”; diamond  $10$  and diamond  $Q$  are not a “*straight flush*” pair. Determine how many ways of picking thirteen cards out of the deck such that all ranks are included but no “*straight flush*” exists in them.

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