
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]


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Ten points are equally spaced on a circle. A graph is a set of segments (possibly empty) drawn between pairs of points, so that every two points are joined by either zero or one segment. Two graphs are considered the same if we can obtain one from the other by rearranging the points.
Let \( N \) denote the number of graphs with the property that for any two points, there exists a path from one to the other among the segments of the graph. Estimate the value of \( N \).

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