Word/phrase for “staring at two things alternately”

Question

Example:

When Liza and Josh told me their crazy plan, I did nothing; just [...].

I thought about glance, but I think glancing is more like looking briefly, rather than staring in bewilderment.

oscillate looks between them. – SrJoven Oct 21 '14 at 3:29 — SrJoven, Oct 21 '14 at 3:29
..."my gaze vacillated between them." – John Deters Oct 21 '14 at 4:01 — John Deters, Oct 21 '14 at 4:01

Kris · Accepted Answer · 2014-10-21 06:37:29Z

If you are alternating, then you are not 'staring.'
In the context, the fact of looking at only one of the two at any point of time is of no significance.

As such, it should be fine to say "staring at them ."

However, if really needed, we could even say "looking alternately at them, utterly bewildered (or such)."

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