
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) $\lim _{x \rightarrow 4} \frac{x^{2}-16}{x^{2}-5 x+4}$
2) $\lim _{x \rightarrow 1} \frac{x^{3}-3 x+2}{x^{3}-x^{2}-x+1}$
3) $\lim _{x \rightarrow 0} \frac{x^{3}-6 x+6 \sin x}{x^{5}}$
4) $\lim _{x \rightarrow 0} \frac{\operatorname{tg} x-x}{x-\sin x}$
5) $\lim _{x \rightarrow \infty} \frac{a x^{2}+b}{c x^{2}+d}$
6) $\lim _{x \rightarrow 0} \frac{\ln \sin 5 x}{\ln \sin 2 x}$

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