
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

a) Compute

$$
\lim _{n \rightarrow \infty} n \int_{0}^{1}\left(\frac{1-x}{1+x}\right)^{n} d x
$$

b) Let \( k \geq 1 \) be an integer. Compute

$$
\lim _{n \rightarrow \infty} n^{k+1} \int_{0}^{1}\left(\frac{1-x}{1+x}\right)^{n} x^{k} d x
$$

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