
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
Assume that the interest rate is \( r \), so that a capital of \( k \) becomes \( k(1 + r)^n \) after \( n \) years. How much do we need to invest to be able to withdraw 1 at the end of year 1, 4 at the end of year 2, 9 at the end of year 3, 16 at the end of year 4 and so on (in perpetuity)?

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