
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
$N$ friends simultaneously learned $N$ pieces of news, with each friend knowing one distinct piece of news. They start calling each other to exchange the news. Each conversation lasts 1 hour, and during a single conversation, any number of pieces of news can be shared.

What is the minimum number of hours required for everyone to know all the pieces of news? Consider the following cases:
a) $N=64$,
b) $N=55$,
c) $N=100$.

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