
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
Ken owns 15 pairs of shoes, consisting of eight identical black pairs, four identical blue pairs, and three pairs of green shoes which are all distinct. If he picks two shoes at random, what is the probability that they are from the same color set with one being a left shoe and the other a right shoe? Express your answer as a common fraction.

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