Emacs attach an action to any key pressed

[Ivanov Dmitry]

Suppose, I have the code:

(defun dummy ()
      (interactive)
      (message "aaa"))

(local-set-key (kbd "<left>") 'dummy)

When you click <left> key in the current buffer, it will print "aaa".

Is it possible to attach this action to any key pressed?

I looked into "Format of Keymaps" and "Searching Keymaps" in Emacs info pages, but found no code examples.