
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
For an upcoming school play, students must decide on costumes. The sixth-graders will pick the color of their hats (red or blue) and the seventh-graders will pick the color of their cloaks (red, blue, or green). Both groups will make their decisions independently, and each possible color is equally likely to be chosen. What is the probability that the hat will be a different color than the cloak? Express your answer as a common fraction.

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