
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
Find the limits:

1) \(\lim_{x \rightarrow \infty} \left(1 + \frac{a}{x}\right)^x\)

2) \(\lim_{n \rightarrow \infty} \left(\frac{n-1}{n+2}\right)^{2n+1}\)

3) \(\lim_{x \rightarrow 0} \sqrt[x]{1 + 3x}\)

4) \(\lim_{x \rightarrow 0} (\cos 2x)^{\frac{1}{\sin^2 x}}\)

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