
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 contains 52 cards. Each card has a value among "1, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king" and a suit among "hearts, diamonds, spades, clubs," such that for each value and suit, the deck contains a unique card with that value and suit. A hand of 5 cards is a choice of 5 cards from this deck, regardless of the order in which the cards are chosen. How many 5-card hands exist that contain four cards of the same value?

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