
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 bank plans to introduce a new fixed deposit service. It is predicted that the deposit amount is directly proportional to the square of the interest rate, with a proportionality constant $k$ ($k>0$). It is known that when the interest rate is $0.012$, the deposit amount is $144$ million. When the loan interest rate is $4.8\%$, the bank can lend out all the absorbed deposits. If the deposit interest rate is set to $x$, where $x \in (0, 0.048)$, what value of $x$ will yield the maximum profit for the bank?

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