
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 that the function \( f(x) \) is defined on \(\mathbf{R}^{+}\), strictly decreases on \(\mathbf{R}^{+}\), and satisfies
$$
f(x) > \frac{1}{x^{2}},
$$
it holds for all \(\mathbf{R}^{+}\) that 
$$
f^{2}(x) f\left(f(x) - \frac{1}{x^{2}}\right) = f^{3}(1).
$$

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

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