Reminiscence means recollecting past events and sleuthing means a detective solving mystery. When writing or talking, can it be delivered like this I met a very old friend, we were reminiscing,or reminiscing the past. They have appointed a sleuthing detective.
Reminiscing implies going over the past, so you shouldn't say reminiscing the past.
There may be uses for sleuthing, but sleuthing detective is too wordy. Sleuth means a detective.
intransitive verb : to act as a detective : search for information
transitive verb : to search for and discover