
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
Suppose the total amount of deposits a bank attracts within a year is directly proportional to the square of the annual interest rate paid to depositors. If the bank lends out 90% of the total deposits at an annual interest rate of 5% immediately after attracting the deposits to earn profits, what should the annual interest rate paid to depositors be set at to maximize the bank's profit?  
(Note: The bank's annual profit is the difference between the annual interest earned on the loans and the annual interest paid to depositors.)

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