
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
A real number  $\alpha$  is given. Find all functions  $f : R^+ \to R^+$  satisfying  $\alpha x^2f\left(\frac{1}{x}\right) +f(x) =\frac{x}{x+1}$  for all  $x > 0$ .

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