
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]


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Under the influence of the market, the economic benefits of a tourism company in the Three Gorges have shown a certain degree of decline. It is now necessary to renovate and upgrade a certain scenic spot to increase the tourism value-added. Through market research, it is found that the tourism value-added y (in million yuan) and the investment x (in million yuan) satisfy the equation $y= \frac {51}{50}x-ax^{2}-ln x+ln 10$, and $\frac {x}{2x-12}\in[1,+\infty)$. When $x=10$, $y=9.2$.

1. Find the analytical expression of $y=f(x)$ and the range of $x$.
2. Find the value of $x$ when the tourism value-added $y$ reaches its maximum.

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