
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
Evaluate the solution and answer provided below. Point out all the errors and shortcomings.

Find the range of the function \( f(x) = x + \frac{2}{x^2} \) for \( x > 0 \).

Solution: According to the inequality between the arithmetic mean and the geometric mean, the following inequality holds:

\[ x + \frac{2}{x^2} \geq \frac{2 \sqrt{2}}{\sqrt{x}} \]

Since the number \( x \) can be chosen arbitrarily large, the interval \( \left[\frac{2 \sqrt{2}}{\sqrt{x}} ; +\infty\right) \) contains arbitrarily small positive numbers, from which we get the answer: the range of the given function is the interval \( (0 ; +\infty) \).

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