
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
Given that the volume of deposits is directly proportional to the square of the deposit interest rate, with a proportionality constant of $k$ ($k>0$) and the loan interest rate is $0.048$, find the value of the deposit interest rate, $x$, that maximizes the bank's profit, given that $x \in (0, 0.048)$.

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