
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 $\alpha \in \mathbb{Q}^{+}$. Determine all functions $f: \mathbb{Q}^{+} \rightarrow \mathbb{Q}^{+}$ such that for all $x, y \in \mathbb{Q}^{+}$, it holds that

$$
f\left(\frac{x}{y}+y\right)=\frac{f(x)}{f(y)}+f(y)+\alpha x.
$$

Here, $\mathbb{Q}^{+}$ denotes the set of positive rational numbers.

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