
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 surveillance service will be installed in a park in the form of a network of stations. The stations must be connected by telephone lines, so that any one of the stations can communicate with all the others, either through a direct connection or through at most one other station.

Each station can be directly connected by a cable to at most three other stations. What is the largest number of stations that can be connected in this way?

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