
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
Given 15 identical balls, find the number of different ways to place the balls into three boxes numbered 1, 2, and 3, such that the number of balls in each box is not less than the number of the box.

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