
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  $f:\mathbb{R}^+\rightarrow\mathbb{R}^+$  such that for all  $x, y\in\mathbb{R}^+$ , 
\[ \frac{f(x)}{y^2} - \frac{f(y)}{x^2} \le \left(\frac{1}{x}-\frac{1}{y}\right)^2\]
( $\mathbb{R}^+$  denotes the set of positive real numbers.)

*(Proposed by Ivan Chan Guan Yu)*

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