
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
Let  $G$  be a connected simple graph. When we add an edge to  $G$  (between two unconnected vertices), then using at most  $17$  edges we can reach any vertex from any other vertex. Find the maximum number of edges to be used to reach any vertex from any other vertex in the original graph, i.e. in the graph before we add an edge.

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