
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 graph, with degree of all vertices not less then  $m \geq 3$ , such that there is no path through all vertices of  $G$  being in every vertex exactly once. Find the least possible number of vertices of  $G.$ 

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