
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
Given a function \( f(x) \) defined on \(\mathbf{R}^{+}\), it satisfies the following conditions:
A. \( f(x) \) is monotonically decreasing on \(\mathbf{R}^{+}\) and \( f(x) > \frac{1}{x^{2}} \);
B. On \(\mathbf{R}^{+}\), \( f^{2}(x) f\left(f(x) - \frac{1}{x^{2}}\right) = f^{3}(1) \).

(1) Find the value of the function \( f(1) \).
(2) Provide a function \( f(x) \) that satisfies the given conditions.

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