
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) \(\lim_{\pi}(\operatorname{tg} x)^{\operatorname{tg} 2x}\)

2) \(\lim_{x \rightarrow +\infty}(\ln x)^{\frac{1}{x}}\)

3) \(\lim_{x \rightarrow 0+} x^{\frac{6}{1 + 2 \ln x}}\)

4) \(\lim_{x \rightarrow 1} x^{\frac{m}{x^2 - 1}}\)

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