Reply to "take a walk"

Kuen, what you need to understand is what David explained when, in reference to the structure "go (and) infinitive", he said something as simple and clear as:

It refers to one complete action, not to an activity.

I think your sentences 1 to 5 above are not grammatically incorrect but, since some of the infinitives following the verb go indicate activities (a continued action) rather than individual actions that can be viewed as having a beginning and an end, the gerund would be more usual. I find these sentences more likely if you wish to use the infinitive:

1'. I need some exercise. I think I'll walk a mile.

2'. I need some exercise. I think I'll walk (instead of taking a taxi).

3'. Let's shop/ hike/ fish.

4'. Let's shop in the store.

5'. I am going to hike in the woods tomorrow morning.

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