
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
Tim plans to secretly switch Nathan's spoon every day for a week as a joke. On Monday, he convinces Peter to do it. On Tuesday, he has three friends (Sam, Jane, or Luke) who could be convinced to do it. On Wednesday, none of these four can participate, but he has six new friends who might help. On Thursday, none of these six are available, but four others are willing. Finally, on Friday, Tim is considering whether to do it himself or to convince one of two new friends (Anne or Bob). How many different combinations of people could Tim involve to switch the spoon each day?

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