
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 $u$ and $v$ be real numbers such that
\[\frac{\sin u}{\cos v} + \frac{\sin v}{\cos u} = 2 \quad \text{and} \quad \frac{\cos u}{\sin v} + \frac{\cos v}{\sin u} = 3.\] Compute
\[\frac{\tan u}{\tan v} + \frac{\tan v}{\tan u}.\]

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