
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
King Arthur's Round Table. Three knights are randomly seated on chairs arranged around King Arthur's court table. What is the probability that there is an empty chair on either side of each knight if:

a) There are a total of 7 chairs?

b) There are a total of \( n \) chairs?

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