
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 rental company has 750 electric cars available for rental, and the daily cost of managing these electric cars is $1700. According to a survey, if the daily rental fee for each electric car does not exceed $90, then all the electric cars can be rented out; if it exceeds $90, for each additional $1 over $90, three more electric cars cannot be rented out. Let the daily rental fee for each electric car be $x$ ($60 \leq x \leq 300$, $x \in \mathbb{N}^{*}$), and let $y$ (in units of dollars) represent the daily net income from renting out electric cars (daily net income is equal to the total income from renting out electric cars per day minus the daily management cost).  
$(1)$ Find the analytical expression of $y$ in terms of $x$;  
$(2)$ Determine at what rental fee per day for each electric car the daily net income will be maximized, and find the maximum value of the daily net income.

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