
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
From a deck of bridge cards, two players have taken the clubs, hearts, and spades numbered 1 to 6 cards, and play the following game with these 18 cards. The player first draws two cards from the deck held by the banker. If the sum of the numbers on the drawn cards is 7, the player wins; if the sum is greater than 7, the player loses; and if the sum is less than 7, the player draws a third card, and wins only if the new number complements the sum of the first two cards to make 7. What is the probability that the player wins?

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