
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
Tim has a more colorful selection in his sock drawer which now contains 12 gray-bottomed socks, 10 white-bottomed socks, and 6 blue-bottomed socks. Every morning, he picks three socks at random. What is the probability that Tim picks either a matching pair of socks or three socks each of different colors?

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