
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 the total production cost $C$ (in ten thousand yuan) of a precision instrument is related to the monthly production volume $x$ (in units) by the function $C=100+4x$, and the maximum monthly production is 15 units. The factory price $p$ (in ten thousand yuan) is related to the monthly production volume $x$ by the function: $p=76+15x-x^2$.  
(1) Find the function relationship between the monthly profit $L$ and the production volume $x$, denoted as $L(x)$.  
(2) At what value of monthly production volume $x$ is the monthly profit $L(x)$ maximized?

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