
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
An ordinary domino tile can be identified as a pair  $(k,m)$  where numbers  $k$  and  $m$  can get values  $0, 1, 2, 3, 4, 5$  and  $6.$  
Pairs  $(k,m)$  and  $(m, k)$  determine the same tile. In particular, the pair  $(k, k)$  determines one tile. 
We say that two domino tiles *match*, if they have a common component. 
*Generalized n-domino tiles*  $m$  and  $k$  can get values  $0, 1,... , n.$  What is the probability that two randomly chosen  $n$ -domino tiles match?

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