
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) \(\lim_{x \rightarrow 1}\left(\frac{1}{\ln x} - \frac{1}{x-1}\right)\)
2) \(\lim_{\varphi \rightarrow \frac{\pi}{2}} (\sec \varphi - \operatorname{tg} \varphi)\)
3) \(\lim_{x \rightarrow 0} x \ln x\)
4) \(\lim_{\alpha \rightarrow \frac{\kappa}{2}} (\pi - 2\alpha) \operatorname{tg} \alpha\)

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