More body parts: The player's left hand

A left hand is a kind of thing.
A left hand is part of every person. 
The lobby is a room.
Jane is a woman in the lobby.
Instead of touching the player's left hand:
	say "Cold as a fish.";

That does not compile. These do work:

Instead of touching jane's left hand:
Instead of touching the left hand which is part of the player:

Why is it that you can’t use “the player’s left hand” here? And is generally safer to refer to parts in a roundabout way - “an X which is part of Y” rather than “Y’s X”?

Also (2): if you want to add hands to the player, how would you do it? Using hands described by a left/right property? Or with “left” and “right” as part of the type name like in the code above? Or some other clever way?

Oh, and (3):

Jessica is a woman. The player is Jessica. 
does the player mean doing something to a left hand: it is very likely.

When you do “x hand”, the game prints “(Jessica’s left hand)” to clarify. Can you change that to “(Your left hand)”? I was naive enough to try "the printed name of a left hand which is part of Jessica is “Z”, but this only results in the game printing “(The yourself’s left hand)”, which was not exactly what I wanted. It does not seem to matter what you use for “Z”. I imagine this some printing the name of activity?

The reason you can use “Jane’s left hand” is that it’s, literally, the name Inform assign to the left hand object it creates as part of creating Jane. However, the name of the corresponding part of the player is (usually) not “the player’s left hand” but “your left hand”.

This is also related to the fact that, if the player is a named character, the naming of the player’s body parts depends on whether the player is named before or after the body parts are attached. In fact, this is documented in Writing with Inform section 4.14. “Assemblies and body parts”:

Nice! Thank you.