
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
Let  $n$  be a given positive integer. How many solutions are there in ordered positive integer pairs  $(x,y)$  to the equation  $$ \frac{xy}{x+y}=n? $$  

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