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Hello. As I was seeking the meanings of 'think of', I've come across this sentence:

1 think of (something) a : to have thoughts about possibly doing (something)
▪ She is thinking of applying to grad school. ▪ He thought of sending an e-mail but decided against it. ▪ She couldn't think of ever leaving her children. ( M-W.com)

Can 'consider' be used interchangeably? For example:

She is considering applying to grad school.

He considered sending an e-mail but decided against it.

So far good, but in the last sentence I don't think consider can be used as it doesn't make any sense to me.

Am I right in thinking that in the first and second sentences consider can be used, but in the third one it cannot be?

Would you help please?
Comments  
You could say "she would never consider leaving her children".
"She couldn't consider ever leaving her children" sounds a bit odd, but then so does "She couldn't think of ever leaving her children".
Thank you Blue Jay. I did not pay attention if "She couldn't think of ever leaving her children" sounds odd, as I came across it in merriam-webster.com. By the way, the rest are OK, right?( By rest I mean, the first and the second sentences)

Edit: Also, how would you rephrase the third sentence?
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The first and second sentences are fine.
I'm not saying #3 is grammatically wrong, just that it is an awkward sentence.
"She could never think of leaving her children" would be less awkward, although it does very slightly change the meaning.
Thank you again, Blue Jay. Would you mind telling me the differences between "She could never think of leaving her children" and "She would never consider leaving her children"?
I didn't notice that I had used would in one sentence and could in the other. As far as these two are concerned could refers to ability, in this case she is, and always will be, unable to consider leaving her children. Would implies that she possesses the ability to think of leaving her children, but will never actually do so. There is no difference in meaning here between think of and consider.
The meaning change I referred to was between
She couldn't think of ever leaving her children and
She could never think of leaving her children.
The first denotes that she could not think about "ever leaving her children".
The second denotes that she could not ever think about "leaving her children".
The practical difference is slight, and both would be understood to mean She would never willingly leave her children.
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Thank you, Blue Jay! I think I see now.