
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
Solve the question of problem 8 for the differential expressions:
a) \(\frac{x \, dy - y \, dx}{x^2 + y^2}\)
b) \(\frac{(x + 2y) \, dx + y \, dy}{(x + y)^2}\).



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