
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 part of a mischievous week, Tom decides to rearrange the books in his friend’s bookshelf every night without getting caught. On Monday, he gets his friend Alice to do it. On Tuesday, he can choose between Bob or Charlie to help him. On Wednesday, Tom decides to bring in three new friends, David, Emily, or Fiona, to do the rearrangement. On Thursday, none of the previous helpers are available, but three others, Gwen, Henry, and Isla, are willing to help. Finally, on Friday, Tom decides to add a twist: either he does it himself, or he convinces his cousin Jack to do it. How many different combinations of people could Tom involve in rearranging the books throughout the week?

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