
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
Square  $\mathcal S$  has vertices  $(1,0)$ ,  $(0,1)$ ,  $(-1,0)$  and  $(0,-1)$ .  Points  $P$  and  $Q$  are independently selected, uniformly at random, from the perimeter of  $\mathcal S$ .  Determine, with proof, the probability that the slope of line  $PQ$  is positive.

*Proposed by Isabella Grabski*

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