
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]


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Consider a generalized domino set where each domino contains two squares, and each square can contain an integer from 0 to 11. Each integer from this range is paired with every integer (including itself) exactly once to form a complete set of dominos. What is the probability that a domino randomly selected from this set will be a $\textit{double}$ (containing the same integer on both squares)?

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