
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 $a$ and $b$ be real numbers such that
\[
\frac{\sin a}{\cos b} + \frac{\sin b}{\cos a} = 2 \quad \text{and} \quad \frac{\cos a}{\sin b} + \frac{\cos b}{\sin a} = 4.
\]
Compute
\[
\frac{\tan a}{\tan b} + \frac{\tan b}{\tan a}.
\]

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