
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
Evaluate the following limits:
1. $\lim_{x \rightarrow 0} \frac{1- \sqrt{x+1}}{x}$
2. $\lim_{x \rightarrow 0} \frac{\operatorname{tg} x}{1-\sqrt{1+\operatorname{tg} x}}$
3. $\lim_{x \rightarrow 1} \frac{2- \sqrt{x}}{3- \sqrt{2x+1}}$
4. $\lim_{x \rightarrow 1} \frac{1- \sqrt{x}}{1- \sqrt[3]{x}}$

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