
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 20 indistinguishable balls to be placed into three boxes labeled 1, 2, and 3, with the requirement that the number of balls in each box is not less than the number corresponding to its label. The number of different ways to distribute the balls is __________.

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