
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 $N$ news items, with each friend learning one piece of news. They started calling each other and sharing the news.

Each call lasts 1 hour, and during one call, any number of news items can be shared.

What is the minimum number of hours required for everyone to know all the news items? Consider the following cases:
a) $N=64$,

b) $N=55$

c) $N=100$.

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