
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 directed graph with infinitely many vertices. It is known that for each vertex the outdegree is greater than the indegree. Let  $O$  be a fixed vertex of  $G$ . For an arbitrary positive number  $n$ , let  $V_{n}$  be the number of vertices which can be reached from  $O$  passing through at most  $n$  edges (  $O$  counts). Find the smallest possible value of  $V_{n}$ .

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