
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
Consider a function \( f \) defined on \( (1, +\infty) \) and taking values in \( (1, +\infty) \) that satisfies the condition: for any \( x, y > 1 \), and \( u, v > 0 \), we have \( f\left(x^{4} \cdot y^{v}\right) \leqslant f(x)^{\frac{1}{4u}} \cdot f(y)^{\frac{1}{4v}} \). Determine all such functions \( f \).

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