
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 jar initially contains $12$ red candies and $8$ blue candies. Terry picks two candies at random. After Terry's turn, one additional red candy is removed from the jar. Then Mary picks two of the remaining candies at random. Determine the probability that Terry and Mary pick candies of the same color, irrespective of order. Express your answer as a simplified fraction $m/n$ where $m$ and $n$ are relatively prime positive integers, then find $m+n$.

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