
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
The Bai Li Du Juan Scenic Area in Qianxi County, during the blooming season of azaleas, experiences heavy traffic. Consequently, the parking lot implements a temporary parking fee system based on the duration of parking. The fee structure is as follows: a charge of 5 yuan for parking not exceeding 1 hour per vehicle, and for each hour beyond the first, an additional 10 yuan is charged (any part of an hour is rounded up to the next full hour). Both Person A and Person B parked their cars in this parking lot, and neither parked for more than 4 hours.

(1) If the probability that Person A parks for up to 1 hour is $\frac{1}{2}$, and the probability of paying more than 15 yuan is $\frac{1}{6}$, find the probability that Person A pays exactly 15 yuan for temporary parking;

(2) If the probability of parking durations for both Person A and Person B in each time slot is the same, find the probability that the sum of their parking fees is 30 yuan.

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