
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
Karcsi has 10 identical balls: 5 are red, 3 are white, and 2 are green. He also has two boxes, one of which can hold 4 balls and the other can hold 6 balls. In how many ways can he distribute the balls between the two boxes? (The arrangement of balls within the boxes does not matter.)

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