
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
In a certain business district parking lot, temporary parking is charged by time period. The charging standard is: each car is charged 6 yuan for parking not exceeding 1 hour, and for the part exceeding 1 hour, the charge is 8 yuan per hour (parts of an hour are rounded up to the next hour). Now, two people, A and B, temporarily parked in this business district, and both of their parking times did not exceed 4 hours. If the probability that A parks for more than 1 hour and up to 2 hours is $\frac{1}{3}$, the probability of parking for more than 2 hours and up to 3 hours is $\frac{1}{4}$, and the probability of parking for more than 3 hours is $\frac{1}{6}$; B's parking duration has the same possibility for each of the first three hours, and the probability of exceeding three hours is $\frac{1}{2}$.  
(1) Find the probability that A pays exactly 6 yuan for parking;  
(2) Find the probability that the sum of the parking fees paid by A and B is 36 yuan.

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