
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 $15$ red candies, $15$ blue candies, and $10$ green candies. Terry picks two candies at random, then Mary picks two of the remaining candies at random. Find the probability that Terry and Mary pick candies of the same color configuration, irrespective of order. The result should be given as a fraction in lowest terms.

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