
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  $N$  be the number of ways to draw 22 straight edges between 10 labeled points, of which no three are collinear, such that no triangle with vertices among these 10 points is created, and there is at most one edge between any two labeled points. Compute  $\dfrac{N}{9!}$ .

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