
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
Answer the following questions:

(1) Let  $a$  be positive real number. Find  $\lim_{n\to\infty} (1+a^{n})^{\frac{1}{n}}.$ (2) Evaluate  $\int_1^{\sqrt{3}} \frac{1}{x^2}\ln \sqrt{1+x^2}dx.$ 35 points

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