
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
There are two-way flights between some of the  $2017$  cities in a country, such that given two cities, it is possible to reach  one from the other. No matter how the flights are appointed, one can define  $k$  cities as "special city", so that there is a direct flight from each city to at least one "special city". Find the minimum value of  $k$ .

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