
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
As a prank, Tim plans to switch Nathan's chair at every dinner over a week. On Monday, he convinces Julia to do it. On Tuesday, he could choose either Sara or Liam to do it. On Wednesday, none of those three can do it, but there are three new people he could convince. On Thursday, the choice of person is determined by who did it on Wednesday—if Wednesday's helper was the first person, then only two specific new people are willing to do it; if it was the second person, three new people are possible; if it was the third person, one specific person can do it. Finally, on Friday, Tim does it himself. How many different combinations of people could Tim involve in this prank through the week?

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