Get a better hand

You are playing a game of poker, and you are dealt the following hand of cards from a shuffled standard poker deck:

A,A,A,6,10.\text{A}\spadesuit, \text{A}\clubsuit, \text{A}\color{#D61F06}{\heartsuit}, 6\color{#D61F06}{\heartsuit}, 10{\color{#D61F06}{\diamondsuit}}.

You put the 66\color{#D61F06}{\heartsuit} and 1010\color{#D61F06}{\diamondsuit} cards aside, and request to be dealt two new cards.

What is the probability that you will improve your hand to a Four of a Kind or a Full House?

Round your answer to three decimal places.

Note: Cards dealt to you are no longer in the deck. The 66\color{#D61F06}{\heartsuit} and 1010\color{#D61F06}{\diamondsuit} cards are put aside; they are not put back into the deck.

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