
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 \( R \) be the rectangle \( 0 \leq x \leq a \), \( 0 \leq y \leq b \). Evaluate \(\int_R e^{f(x, y)} \, dx \, dy\), where \( f(x, y) = \max\left(\frac{b^2 x^2}{a^2}, \frac{a^2 y^2}{b^2}\right) \).

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