
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 single-player card game involves the following rules: 6 pairs of different cards are placed in a bag. The player randomly draws cards from the bag one at a time and returns the card back to the bag. However, when a pair of matching cards is drawn, those cards are set aside. If the player draws three cards each time, and none of the three cards form a pair, the game ends. Otherwise, the drawing continues until there are no cards left in the bag. Given that the probability of the bag being empty is $\frac{p}{q}$, where $p$ and $q$ are coprime positive integers, find $p+q$.

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