
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) \(\lim_{x \rightarrow 2}\left(3x^{2}-2x+7\right)\)
2) \(\lim_{x \rightarrow 3} \frac{3x^{2}-1}{2x^{3}+6x^{2}-5}\)
3) \(\lim_{x \rightarrow 2} \frac{x-2}{x^{2}+3x-1}\)
4) \(\lim_{x \rightarrow 3} \frac{x^{2}-2x+1}{x-3}\)
5) \(\lim_{x \rightarrow 0} \frac{5x^{3}+2x^{2}-x}{3x}\)
6) \(\lim_{x \rightarrow 4} \frac{x^{2}-6x+8}{x^{2}-5x+4}\)
7) \(\lim_{x \rightarrow 1} \frac{\sqrt{1+8x}-3}{\sqrt{4x}-2}\)
8) \(\lim_{x \rightarrow 0} x \sin \frac{1}{x}\)
9) \(\lim_{x \rightarrow \infty} \frac{2x^{3}-x+1}{5x^{3}+2x^{2}-1}\)
10) \(\lim_{n \rightarrow \infty} \frac{\sqrt{n^{2}+1}+\sqrt{n}}{\sqrt[4]{n^{3}+n}-n}\)

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