
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. \(\lim _{x \rightarrow 1}(1-x) \operatorname{tg} \frac{\pi x}{2}\)
2. \(\lim _{x \rightarrow \frac{\pi}{4}}\left(\frac{\pi}{4}-x\right) \operatorname{cosec}\left(\frac{3}{4} \pi+x\right)\)
3. \(\lim _{x \rightarrow+\infty} x \operatorname{arcctg} x\)
4. \(\lim _{x \rightarrow-\infty} x\left(\frac{\pi}{2}+\operatorname{arctg} x\right)\)

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