
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
Given that the probability that it will not rain in area A is P<sub>1</sub> (0<P<sub>1</sub><1) and the probability that it will not rain in area B is P<sub>2</sub> (0<P<sub>2</sub><1), calculate the probability that it will rain in both areas.

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