
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 supermarket plans to order a type of yogurt monthly, with the same daily purchase quantity. The cost of purchasing each bottle is $4, and the selling price is $6. Unsold yogurt is sold at a reduced price of $2 per bottle on the same day. Based on past sales experience, the daily demand is related to the highest temperature of the day (in degrees Celsius). If the highest temperature is not less than 25 degrees, the demand is 500 bottles; if the highest temperature is in the range [20, 25), the demand is 300 bottles; if the highest temperature is less than 20, the demand is 200 bottles. To determine the ordering plan for June, the highest temperature data for each day in June of the past three years were collected, resulting in the frequency distribution table below:

| Highest Temperature | [10,15) | [15,20) | [20,25) | [25,30) | [30,35) | [35,40) |
|---------------------|---------|---------|---------|---------|---------|---------|
| Days                | 2       | 16      | 36      | 25      | 7       | 4       |

Estimate the probability of the highest temperature falling within each interval based on the frequency.

(1) Calculate the probability that the demand for this type of yogurt in June does not exceed 300 bottles in a day.

(2) Assuming the profit from selling this type of yogurt in June in a day is $Y (in units of currency), when the daily purchase quantity in June is 450 bottles, list all possible values of $Y and estimate the probability that $Y is greater than zero.

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