
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
In a group of 8 people, each with a different number of internet friends within the group, and where Adam and Benin cannot be friends, and none of them has an internet friend outside this group, calculate the number of different ways the friendships can be formed if exactly one person has no internet friends and no one is friends with all the others.

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