
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  $$ \lim_{n\to\infty}n\int^1_0\left(\frac{1-x}{1+x}\right)^ndx. $$  b) Let  $k\ge1$  be an integer. Compute  $$ \lim_{n\to\infty}n^{k+1}\int^1_0\left(\frac{1-x}{1+x}\right)^nx^kdx. $$  

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