
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
Gretchen now has ten socks, three of magenta, three of cyan, two of black, and two of white. She again randomly draws four socks. What is the probability that she either gets exactly one pair of socks with the same color (and the other two socks are of different colors) or gets two pairs of socks?

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