
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 customized deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and three distinct colors for the suits: $\spadesuit$ (black), $\heartsuit$ (red), $\diamondsuit$ (blue). Each color group contains equal numbers of the 12 suits (not typical suits, just color labeled), and there are approximately 4 cards of each color for every rank, with each card having a unique rank within its color. If the deck is randomly arranged, what is the probability that the top three cards are all $\spadesuit$s?

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