
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
In a kingdom, there are eight cities. The king wants to construct a road system such that it is possible to travel from any city to any other city, passing through at most one intermediate city, and no more than $k$ roads lead out of each city. For which values of $k$ is this possible?

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