
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
\[\frac{\sin^2 a}{\cos^2 b} + \frac{\sin^2 b}{\cos^2 a} = 2 \quad \text{and} \quad \frac{\cos^3 a}{\sin^3 b} + \frac{\cos^3 b}{\sin^3 a} = 4.\]Compute
\[\frac{\tan^2 a}{\tan^2 b} + \frac{\tan^2 b}{\tan^2 a}.\]

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