
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 asymptotes of the following curves:
1) \( y = \frac{x^{2}-6x+3}{x-3} \);
2) \( y = xe^{x} \);
3) \( y = x + \frac{\sin x}{x} \);
4) \( y = x \operatorname{arcctg} x \);
5) \( y = \ln(4 - x^{2}) \);
6) \( y = \sqrt[3]{x^{3} - 6x^{2}} \)

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