
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 contains $8$ red candies and $12$ blue candies. Terry and Mary each randomly pick two candies from the jar, one after the other, without replacement. Determine the probability that they pick the same color combination, irrespective of order, in its simplest form as a fraction $m/n$, where $m$ and $n$ are coprime positive integers. Find the sum $m+n$.

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