
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 have a round pizza. It is allowed to make no more than 100 straight cuts without rearranging the pieces until the cutting is completed, after which all the resulting pieces should be distributed among all friends so that each receives the same total area of pizza. Are such cuts possible if a) $\mathrm{N}=201$; b) $\mathrm{N}=400$?

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