
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 $f(x)$ be a function from positive real numbers to real numbers satisfying the equation
\[ xf(y) - 2yf(x) = f \left( \frac{x}{y} \right) \]
for all positive real numbers $x$ and $y.$ Determine all possible values of $f(50).$

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