In the recently proposed problems of optimal actuation for channel and source
coding,  actions are taken at the encoders or at the decoders with the aim of
either acquiring side information in an efficient way or of controlling,
or probing, effectively the channel state. In this paper, the problem of
embedding information on the actions is introduced for both the source and the
channel coding set-ups. In both cases, a decoder is present that observes only a
function of the actions, and wishes to recover a lossy version of the source or
a part of the message. Various single-letter characterizations are derived.
Examples are provided that shed light into the trade-off between the rate of
information embedding and the effectiveness of the actions for source or channel
coding.