
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 certain city's finance department allocated a special fund of $100$ million yuan, which was used for two ecological maintenance projects: planting greenery and protecting the environment, and pollution treatment. The ecological benefits brought by the planting and greening project within five years can be expressed as a function of the investment amount $x$ (unit: million yuan) as $y_{1}$ (unit: million yuan): $y_{1}=\frac{{27x}}{{10+x}$. The ecological benefits brought by the pollution treatment project within five years can be expressed as a function of the investment amount $x$ (unit: million yuan) as $y_{2}$ (unit: million yuan): $y_{2}=0.3x$. Let the funds allocated to the planting and greening project be $x$ (unit: million yuan), and the total ecological benefits brought by the two ecological projects within five years be $y$ (unit: million yuan).
$(1)$ Express $y$ as a function of $x$;
$(2)$ To maximize the total ecological benefits $y$, how should the investments in the two ecological projects be distributed?

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