
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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During an underwater archaeology activity, a diver needs to dive 50 meters to the seabed to carry out archaeological work. The oxygen consumption includes the following three aspects: 
1. The average descent speed is $x$ meters per minute, and the oxygen consumption per minute is $\frac{1}{100}x^2$ liters;
2. The diver's working time on the seabed ranges from at least 10 minutes to a maximum of 20 minutes, with an oxygen consumption of 0.3 liters per minute;
3. When returning to the surface, the average speed is $\frac{1}{2}x$ meters per minute, with an oxygen consumption of 0.32 liters per minute. The total oxygen consumption of the diver in this archaeological activity is $y$ liters.

(1) If the working time on the seabed is 10 minutes, express $y$ as a function of $x$;

(2) If $x \in [6,10]$ and the working time on the seabed is 20 minutes, find the range of the total oxygen consumption $y$;

(3) If the diver carries 13.5 liters of oxygen, what is the maximum number of minutes the diver can stay underwater? (Round the result to the nearest integer).

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