
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 distinct ordered pairs $(x,y)$ where $x$ and $y$ are positive integers satisfying both equations $(xy)^4 - 2x^2y^2 + 1 = 0$ and $x+y=4$.
A) 0
B) 1
C) 2
D) 3
E) More than 3

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