
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 PQRS has sides of length 8, and it is split into four rectangular regions by two line segments, one parallel to PQ and another parallel to QR. Determine the number of ways in which these lines can be drawn so that the area of each of the four rectangular regions is a positive integer.

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