So, this is a pretty common way I see DMs resolve actions. The player asks to make a check, or states what they want to accomplish but not what their character does to try and accomplish it and the DM calls for a check. Then based on the results of the check, the DM comes up with a narrative explanation for what the character must have done to achieve that outcome.
yeah someone up thread asked me if I did that... I don't see a reason to add details no one cares about most times. "I check for traps" "traps?" holding up a d20, and "I carefully check the door for contact poison's, hidden needles, pullies mechanisms and wires" all work in my game and I will match the energy as best I can as a DM "you find one" "yup" "'as you are checking you come across a thin wire connecting the door knob and something in the frame"
I don't normally add to the player. Some times this leads to some time latter 2 of us (sometimes 2 players sometimes 1 player 1 DM) having discussed a more detailed thought and we saw it differently in our minds.
I don’t care for this approach because it leaves the in-fiction action ambiguous until after its success or failure is determined, and it usually requires the DM to be the one to decide what the character did, which I see as an overstepping of their role.
except again it isn't needed.
in the perception example lets use 3 different rooms that the PC says "Can I use perception" as they open the door
room 1 has a hidden pit trap in the center under the rug
room 2 has a hidden assassin in the shadows
room 3 has a secret false brick with treasure behind it.
I let the player roll the skill (even though you would not)
"Looking more closely you see the rug is sagging a slight bit, it looks like a pit trap" or "no even looking carefully you don't see the HUGE danger...the tarrasque hit behind the table leg perfectly" then laugh
"as you study the room closer for a second you see a form hiddden in the shadows... she's cute, but she has a knife... so you know just your type" or "sorry, you missed all 17 mimics...good luck"
"as you look there is something on the wall, you think a trigger or false brick" or "Oh boy you are as perseptive as a deaf bat... you got nothing"
now you may notice I didn't give him any action he didn't take in any... but I was more then a bit sarcastic on each fail
I have occasionally seen the player actually suggest a narrative explanation for the result of their check, but even then they usually look to the DM for confirmation that their description is valid, and often the DM will add their own narrative detail. This is, for example, how Matt Mercer does it.
I dislike a lot of online streamed games because of the DM adding descriptions to the players actions... sometimes even changing the action.
Personally, I prefer the player to give the narrative explanation first, then decide if a roll is even necessary based on that narrative explanation. In this setup, the roll doesn’t determine how well you did; if you say you do it, you do it, and the check is used to determine if any potential consequences of what you did occur.
I still don't see the difference between a detailed explanation of what they do or just giving a skill name or feature name and intent