
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
1. Find \(\lim_{x \to \infty} \frac{x^2}{e^x}\).

2. Find \(\lim_{k \to 0} \frac{1}{k} \int_{0}^{k} (1 + \sin{2x})^{1/x} \, dx\).

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