
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
a) A hotel guest once arrived without money but possessed a silver chain consisting of seven links. The hotel owner agreed to let the guest stay for a week on the condition that they give him one link of the chain as payment each day. What is the minimum number of links that need to be cut so that the owner of the chain can pay the hotel owner daily for seven days (possibly taking back previously given links and giving different ones instead)?

b) The chain consists of 2000 links. What is the minimum number of links that need to be cut so that any number of links from 1 to 2000 can be obtained by taking some number of the resulting pieces?

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