Re: Political Career. Can't promote Cause.

It is, essentially, a glitch.  Promote cause is for either the Charity Organizer or before you chose which branch of politics you want to take.  It looks like you are in the Politician branch, so no, Promote Cause will not show for you because that is not an interaction allowed in the Politician Branch.  Normally I have only seen this immediately after choosing to go into the Politician Branch (level 5 - Civil Servant) when you chose to Work from Home before the promotion goes through.

At the end of the day, you just have to ignore that task.  If you need the money from the task, get Confident and head to Uptown and make a Confident speech as I am fairly certain that giving speeches also generates money (though at this point I cannot recall for complete certain).

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EDIT:  You might want to try the "Promote Policies" social interaction as that is the Politician Branch equivalent of "Promote Cause"; however, I have no idea if that would work or not.  Just a thought.