
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
Determine the number of points with positive integer coordinates that lie within or on the boundary of the region defined by the inequality \( xy \leq 12 \) in the \(xy\)-plane.
A) 30
B) 32
C) 35
D) 36
E) 40

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