
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
Fifteen freshmen are sitting in a circle around a table, but there are only six copies of today's handout available. Each freshman should get at most one handout, and any freshman who does not receive a handout should be able to read from a neighbor who has one. The freshmen are distinguishable but the handouts are not. How many ways are there to distribute the six handouts subject to the above conditions?

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