
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  $\mathcal{P}$   be a convex polygon with  $50$  vertices. A set  $\mathcal{F}$   of diagonals of  $\mathcal{P}$  is said  to be *$minimally friendly$* if any diagonal  $d \in \mathcal{F}$  intersects at most one other diagonal  in  $\mathcal{F}$   at a point interior to  $\mathcal{P}.$  Find the largest  possible number of  elements  in a  $\text{minimally friendly}$  set  $\mathcal{F}$ .

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