
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
A country with  $n$  cities has some two-way roads connecting certain pairs of cities. Someone notices that if the country is split into two parts in any way, then there would be at most  $kn$  roads between the two parts (where  $k$  is a fixed positive integer). What is the largest integer  $m$  (in terms of  $n$  and  $k$ ) such that there is guaranteed to be a set of  $m$  cities, no two of which are directly connected by a road?

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