
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
Affected by the market, a tourism company in the Three Gorges has experienced a certain degree of economic downturn. Now, it is necessary to renovate and upgrade a certain scenic spot to increase the tourism value. After market research, the added value of tourism $y$ (in ten thousand yuan) and the investment $x$ (in ten thousand yuan) satisfy the relationship $y= \frac{51}{50}x - ax^2 - \ln x + \ln 10$, and $\frac{x}{2x-12} \in [1, +\infty)$. When $x=10$, $y=9.2$.
(1) Find the explicit formula for $y=f(x)$ and the range of values for the investment $x$:
(2) Find the value of $x$ when the added value of tourism $y$ reaches its maximum.

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