
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 is planning to introduce a new term deposit service. It is predicted that the volume of deposits is directly proportional to the deposit rate, with a proportional constant $k$ (where $k > 0$). The loan interest rate is set at 6%, and the bank expects to loan out all the deposits it receives.
(1) If the deposit interest rate is $x$, where $x \in (0, 0.06)$, express the relationship between the deposit volume $g(x)$ and the interest $h(x)$ that the bank must pay to depositors as functions of the deposit interest rate $x$. 
(2) What should the deposit interest rate be set at for the bank to achieve maximized profits?

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