
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   $\mathcal{L}$  be a finite collection of  lines in the plane in general position (no two lines in  $\mathcal{L}$  are parallel and no three are concurrent). Consider the open circular discs inscribed in the triangles enclosed by each triple of lines in  $\mathcal{L}$ . Determine the number of such discs intersected by no line in  $\mathcal{L}$ , in terms of  $|\mathcal{L}|$ . 

*B. Aronov et al.*

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