You dont need to do steps 1 and 3 as that wont do anything except break the log chain.

If you have somewhere big enough to store the backup.bak file, move it there for now. Then take a full backup to a timestamped bak file, then do your transaction logs to timestameped trn files.

Ensure that you have a routine in place that pulls the files to a tape drive or some other backup media, so that you have recoverability going back in time as well, you never know when you might need a backup from.

In my signature there is a link to Ola's website, there is a very good comprehensive script which will do the backups for you to individual files.