
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
There are 10 identical red balls, 15 identical black balls, and 20 identical white balls. These balls are to be distributed among two boys and one girl, with each boy receiving at least two balls of each color and the girl receiving at least three balls of each color. How many different ways are there to distribute the balls to these three students?

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