
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
Let \( x \) and \( y \) be positive real numbers, and let \( \theta \neq \frac{n \pi}{2} \) (where \( n \) is an integer). If \( \frac{\sin \theta}{x}=\frac{\cos \theta}{y} \), and \( \frac{\cos ^{4} \theta}{x^{4}}+\frac{\sin ^{4} \theta}{y^{4}}=\frac{97 \sin 2 \theta}{x^{3} y+y^{3} x} \), then find the value of \( \frac{y}{x}+\frac{x}{y} \).

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