
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 piece of news. They started calling each other and exchanging news.

Each conversation takes 1 hour. During a conversation, any number of pieces of news can be exchanged.

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

b) $N=55$,

c) $N=100$.

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