
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
John now has 15 marbles of different colors, including two red, two green, and two blue marbles. In how many ways can he choose 5 marbles if exactly two of the chosen marbles must be either red, green, or blue, and no two marbles of the same color can be chosen?

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