
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
Find all functions \( f: \mathbf{Q}_{+} \rightarrow \mathbf{Q}_{+} \) such that for all \( x, y \in \mathbf{Q}_{+} \), the following equation holds:
$$
f\left(x^{2} f^{2}(y)\right)=f^{2}(x) f(y) .
$$

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