
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 the equations
\[\frac{\sin x}{\cos y} + \frac{\sin y}{\cos x} = 2 \quad \text{and} \quad \frac{\cos x}{\sin y} + \frac{\cos y}{\sin x} = 3,\]
find \(\frac{\tan x}{\tan y} + \frac{\tan y}{\tan x}\).

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