
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) \(\lim _{x \rightarrow 2} \frac{x^{4}-16}{x^{3}+5x^{2}-0x-16}\)

2) \(\lim _{x \rightarrow a} \frac{x^{n}-a^{n}}{x^{n}-a^{n}}\)

3) \(\lim _{x \rightarrow 0} \frac{e^{2x}-1}{\sin x}\)

4) \(\lim _{x \rightarrow 0} \frac{1-\cos(ax)}{1-\cos(bx)}\)

5) \(\lim _{x \rightarrow+\infty} \frac{e^{x}}{x^{4}}\)

6) \(\lim _{x \rightarrow \frac{\pi}{2}} \frac{\tan x}{\sec x}\)

7) \(\lim _{x \rightarrow \alpha} \frac{x-\sin x}{x+\sin(x/x)}\)

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