
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
If \( x \) and \( y \) are any real numbers, \( x \neq 0, y \neq 0 \),

$$
3\left(\frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}}\right)-8\left(\frac{x}{y}+\frac{y}{x}\right)+10 \geq 0
$$

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