取る: trying to get a box and taking a break
Compare a box as the goal of standing on tiptoe with an actual break in 休憩を取る. Read the object and activity without assuming the box was obtained or turning a break into approved leave.
Standing on tiptoe to get a box
取る (とる) can describe getting an object. 「棚の上の箱を取るために背伸びした。」 means “I stood on tiptoe to get the box from the shelf.” 箱を identifies the object sought, and 取るために states the purpose of standing on tiptoe.
The action actually reported is 背伸びした: standing on tiptoe. The goal of getting the box is different from an achieved acquisition. The sentence alone does not settle whether the box was obtained or remained out of reach.
休憩を取る: taking a break in the shade
「疲れたので木陰で休憩を取りました。」 means “I was tired, so I took a break in the shade of a tree.” 休憩を取る is the combination for taking a break. Its object is an activity rather than an item received by hand.
疲れたので gives the reason for the break, and 木陰で gives its location. 取りました reports an actual past action. Taking this break should not be interpreted as receiving a box or obtaining approval for a leave request.
Read the object together with the purpose expression
In the first sentence, 箱を取る is the goal of another action; in the second, 休憩を取る is the activity performed. A fixed translation of 取る as receiving a physical object would miss the break example. The object helps distinguish acquiring a box from taking a rest.
ために states a purpose, whereas 取りました reports taking the break. Leave the box's acquisition undecided while preserving the actual break. Whether a workday ended or leave was approved is not supplied by either sentence.
What does 取る combine with in 「箱を取るために」 and 「休憩を取りました」?
Show the answer and why
It combines first with the box as the intended object, giving the purpose of standing on tiptoe. It then combines with a break as an activity actually taken. The first sentence does not establish whether the box was obtained.