In UCI you would send a comment 'go infinite' after setting up the position to analyse with the usual 'position ... moves ...' command. Terminate with 'stop' before sending any other commands.
In CECP the command is 'analyze', and you terminate that with 'exit' (which brings you back into force mode). In CECP it is allowed to send 'setup' commands, moves and 'undo' during the analysis, after which the engine starts searching the new position.
In both cases the 'thinking output' is as usual. Meaning that in CECP you might need to send a 'post' command to make sure it will be given.