
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  $10^{2015}$  planets in an Intergalactic empire. Every two planets are connected by a two-way space line served by one of  $2015$  travel companies. The Emperor would like to close  $k$  of these companies such that it is still possible to reach any planet from any other planet. Find the maximum value of  $k$  for which this is always possible. 

(D. Karpov)



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