
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) \( \lim_{x \rightarrow 0} \frac{\sin 3x}{x} \)

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

3) \( \lim_{x \rightarrow 1} \frac{\cos \frac{\pi x}{2}}{1-x} \)

4) \( \lim_{x \rightarrow -2} \frac{x^{2}-4}{\operatorname{arctg}(x+2)} \)

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