How can I stuff in a new window of an existing screen session?

Hi all,

I would really appreciate your help with this.

Suppose that I start a session like so:
$screen -dmS mysession

I would like a command that, at the same time:
1. Will create a new window named "newwindow" inside mysession
2. Will stuff "command" inside that new window

Any ideas how to do that?

Thank you in advance

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PS. What I have tried and does not work:

$screen -S mysession -X stuff "command"
That will stuff "command" inside the *prexisting* window inside
mysession, but I would like a new window..

$screen -S mysession -X screen "command"
This opens a new window, and runs the command "command". However, I
don't want a command, I want to stuff. Furthermore this does not name
the new window.