Your summary is incorrect. Step 3 doesn't match what GPT-4 actually said:
> When the 7-minute hourglass runs out, don't flip it yet, but note that the 4-minute hourglass has now been running for 3 minutes on its second run. (This marks 7 minutes.) When the 4-minute hourglass runs out again, flip the 7-minute hourglass. (This marks 8 minutes.)
Notice that GPT-4 says not to flip H7 when it runs out, which is a mistake.
> When the 7-minute hourglass runs out, don't flip it yet, but note that the 4-minute hourglass has now been running for 3 minutes on its second run. (This marks 7 minutes.) When the 4-minute hourglass runs out again, flip the 7-minute hourglass. (This marks 8 minutes.)
Notice that GPT-4 says not to flip H7 when it runs out, which is a mistake.