
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 graph has  $ n$  vertices and  $ \frac {1}{2}\left(n^2 \minus{} 3n \plus{} 4\right)$  edges. There is an edge such that, after removing it, the graph becomes unconnected. Find the greatest possible length  $ k$  of a circuit in such a graph.

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