
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
Given that x ∈ (0, 4) and y ∈ (0, 4):

1. If x ∈ N+ and y ∈ N+, and x and y are the lengths of the sides of a rectangle with area S, find the probability that S < 4.
2. If x ∈ R and y ∈ R, find the probability that the difference between the two numbers is not greater than 2.

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