
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
The mythical "Multi-Headed Hydra" consists of several heads and necks, with each neck connecting two heads. With every sword strike, you can sever all necks connected to a particular head $A$, but new necks will immediately grow from head $A$ to all heads that were not originally connected to it (each head is connected by only one neck). The Hydra is defeated only when it is cut into two disconnected parts. Find the smallest natural number $N$ such that for any Hydra with 100 necks, it can be defeated in no more than $N$ strikes.

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