
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
Imagine an extended set of domino tiles where each tile is again composed of two squares, and now integers from 0 to 12 are represented on each square and still each integer is paired with every integer exactly once, including itself, to form a full set. What is the probability that a domino randomly selected from this new set will be a $\textit{double}$?

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