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When rain pours, you should immediately put up your umbrella.

Drizzle is pouring, so it's good to put the umbrella over the head.

Are the two sentences correct?

Please help me.
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When it rains, you should immediately put up your umbrella.

It's drizzling, so it's good to put up your umbrella. -- it is impossible for drizzle to pour.
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Thank you Mister Micawber.

I think it is also impossible to pour "rain". Am I right?
Yes, you can use 'pour' with 'rain' when you want to make a point of how heavy the rainfall is-- but normally we don't need both words: It's raining hard = it's pouring. One case in which you will see both words together is when it is modified: The rain was pouring down hard when I stepped out of the taxi.