
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, the temporary parking fee is charged by time period. The fee is 6 yuan for each car if the parking duration does not exceed 1 hour, and each additional hour (or a fraction thereof is rounded up to a full hour) costs 8 yuan. It is known that two individuals, A and B, parked in this parking lot for less than 4 hours each.
(i) If the probability that individual A's parking duration is more than 1 hour but does not exceed 2 hours is $\frac{1}{3}$, and the probability that they pay more than 14 yuan is $\frac{5}{12}$, find the probability that individual A pays exactly 6 yuan for parking.
(ii) If both individuals have an equal probability of parking within each time interval, find the probability that the total parking fee paid by A and B is 36 yuan.

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