
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 $x$ and $y$ are nonzero real numbers, $\theta \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$, and they satisfy the following simultaneously:
1. $\frac{y}{\sin\theta} = \frac{x}{\cos\theta}$
2. $\frac{10}{x^{2} + y^{2}} = \frac{3}{xy}$

Find the value of $\cos\theta$.

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