
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
David throws six identical darts, and each hits one of five identical dartboards on the wall. After throwing the six darts, he lists the number of darts that hit each board, from greatest to least. Further, at least one dartboard must always have at least one dart more than any of the others. How many different lists are possible?

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