
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) \(\lim _{x \rightarrow 2}\left(\frac{1}{x-2}-\frac{4}{x^{2}-4}\right)\)

2) \(\lim _{x \rightarrow +\infty}\left(x-\sqrt{x^{2}+5x}\right)\)

3) \(\lim \left(\sqrt{\operatorname{tg}^{2} \alpha+\sec \alpha-\operatorname{tg} \alpha}\right)\)

4) \(\lim _{x \rightarrow 0}(2 \operatorname{cosec} 2x - \operatorname{ctg} x)\)

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