
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
Six boxes are numbered from 1 to 6. In how many ways can 20 identical balls be distributed among these boxes

a) so that no box is empty?

b) if some boxes can be empty?

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