
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
Using theorem 5 from the given section, find the limits:
1) \(\lim _{x \rightarrow 0} \frac{\sin 3 x}{5 x}\);
2) \(\lim _{x \rightarrow 0} \frac{\sin 9 x}{\sin 5 x}\);
3) \(\lim _{x \rightarrow 0} \frac{\cos x - \cos 2 x}{x^{2}}\);
4) \(\lim _{x \rightarrow 0} \frac{\tan p x}{\tan q x}\);
5) \(\lim _{x \rightarrow 0} \frac{\ln (1+3 x)}{7 x}\);
6) \(\lim _{x \rightarrow 0} \frac{\arcsin 5 x}{\arcsin 2 x}\).

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