
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
During a certain period, the probability of rain in place A is 0.2, and the probability of rain in place B is 0.3. The rain in both places is mutually independent. Calculate the probability during this period for the following events:
(1) It does not rain in both places A and B;
(2) It rains in exactly one of places A or B;
(3) It rains in at least one of places A or B;
(4) It rains in at most one of places A or B.

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