
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 has 15 marbles of different colors, including two reds, two greens, and two blues. In how many ways can he choose 5 marbles, if exactly two of the chosen marbles must be among the red, green, and blue marbles (including the possibility of choosing two marbles of the same color)?

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