
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
Misha arrived in a country with \( n \) cities, and every two cities are connected directly by a road. He plans to travel starting from a certain city visiting several cities, without visiting any city more than once. Each time Misha travels on a road, the president destroys \( k \) roads leading out of the city to which the road leads. (If there are not enough remaining roads, the president destroys all remaining roads except the one Misha is traveling on.) What is the maximum number of cities Misha can visit, regardless of the president's actions?

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