
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
During an underwater archaeological activity, a diver needs to dive to a depth of $30$ meters to perform tasks. The diver's oxygen consumption consists of the following three aspects: $(1)$ During the descent, the average speed is $x$ meters per minute, and the oxygen consumption per minute is $\frac{1}{90}x^{2}$ liters; $(2)$ The underwater tasks require $10$ minutes, with oxygen consumption of $0.3$ liters per minute; $(3)$ During the ascent, the speed is $\frac{1}{2}x$ meters per minute, with oxygen consumption of $0.2$ liters per minute. Let $y$ denote the diver's total oxygen consumption in liters for this archaeological activity.
$(1)$ Express $y$ as a function of $x$;
$(2)$ If $x \in [4,8]$, find the range of total oxygen consumption $y$.

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