
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
Keisha's basketball team is updating their uniform style. The ninth-graders will choose the color of the socks (red or blue), and the tenth-graders will decide the color of the headbands (red, blue, or green). Each group makes their choice independently and each color is equally likely to be chosen. What is the probability that the socks will be a different color than the headband?

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