
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
In a jar, there are 15 red candies and 15 blue candies. Terry picks three candies at random, then Mary picks two candies from the remaining candies at random. Find the probability that Terry and Mary pick candies of the same color, irrespective of order, expressed in simplest form as $m/n$. Calculate $m+n$.

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