In Collins COBUILD English Usage:
for
If something is for someone, they are intended to have it or benefit from it.
He left a note for her on the table.
She held out the flowers and said, 'They're for you.'
I am doing everything I can for you.
You use for in front of a noun phrase or -ing form when you state the purpose of an object, action, or activity.
Some planes are for internal use, others for international flights.
The mug had been used for mixing flour and water.
You use for in front of a noun phrase when you are saying why someone does something.
We stopped for lunch by the roadside.
I went to the store for a newspaper.
Be Careful!
Don't use 'for' with an -ing form when you saying why someone does something.
Don't say, for example, 'He went to the city for finding work'.
You say 'He went to the city to find work' or 'He went to the city in order to find work'.
People would stroll down the path to admire the garden.
He had to hurry in order to reach the next place on his schedule.
Ok, the dictionary says that "I went to the store for a newspaper." expressing a reason (The reason I went to the store is that I want to buy a newspaper).
However, I would say that "I went to the store for a newspaper." also expresses a purpose (I went to the store with a purpose, that is I want to buy a newspaper)
So, How to tell which sentences expressing purposes & which ones expressing reasons?
For example, I do we know that this sentence "I went to the store for a newspaper." expresses a reason but not a purpose?? a reason & a purpose are almost the same.
Note: we need to know that because the dictionary says:
Don't use 'for' with an -ing form when you saying why someone does something.