Mongo Query to Match on one of three fields and then alter the field that was matched on

I am struggling to find a way to create a query that will allow me to match one of three fields (field_A, field_B, field_C) and then alter the field that was matched on, using $addFields.

Example Document:
{
field_A: 5,
field_B: 10,
field_C: 15
}

If I check for a document that has a value of 10 in one of those three fields, I’d like it to match the document above and then allow me to alter the proper field that was matched on with $addFields, in this case it would be field_B. Is this possible?

So something around the logic of:

If match field_A, then do this
If match field_B, then do this
If match field_C, then do this
etc.

I would approach that with:

The query part of the update is obviously:

{ "$or" : [ {"field_A":10} , {"field_B":10} , {"field_C":10} ] }

And the update with aggregation could be:

[ { "$set" : {
  "field_A" : { "$cond" : [ "$eq" : [ "$field_A" , 10 ] , new_value , "$field_A" ]  }
  "field_B" : { "$cond" : [ "$eq" : [ "$field_B" , 10 ] , new_value , "$field_B" ] }
  "field_C" : { "$cond" : [ "$eq" : [ "$field_C" , 10 ] , new_value , "$field_C" ] }
} } ]

You requirement was not clear about what to do if more than one field matches, so my solution update all the fields that match.