
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
Two cities, A and B, are located in the lower reaches of the Yangtze River. According to more than a hundred years of records, the proportion of rainy days in a year is 20% for city A and 18% for city B. The number of days when both cities experience rain accounts for 12%. Calculate:

(1) The probability that city A also experiences rain when city B is rainy;
(2) The probability that at least one of the two cities experiences rain.

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