using paper in a phone interview

Friends
Thanks so much for being such a supportive community. I seem to have a strange problem and was wondering if someone here could help me out.
Basically, I think well on a paper / whiteboard and only then I code well. If not, I find it hard to manage all details / "picture " in my head and mess up badly.
I had this trouble come up with even basic question of reversing linked list in a FB phone interview.
I took so long (20 mins) to cover all edge cases and get the indices long. The same solution, had I drawn a list side by side and processed would barely take 10 mins. As a result, ran short of time for the second one.

I had asked the recruiter if its advisable to use paper/ pen and she had suggested not to.

Any ideas? Any one else who overcame same trouble, any help is appreciated.

Thanks a lot!

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