It depends what action you are talking about. If her actions caused you damages, you should have a good claim to recover them. Without the authority, she cannot sign on your behalf, and you should bring it up to her supervisor in writing. This may be a case of putting them on noice in case a future problem arises or perhaps this is a notice for you that you may need to change advisors.
Legal Disclaimer: Mr. Carlson is licensed to practice law in California. The response herein is not legal advice and does not create an attorney/client relationship. The response is intended as legal education and to provide general information about the matter within the question.
Whether or not this constitutes forgery, it would be against the industry rules if your advisor was a registered representative registered with FINRA or a state or federally registered investment advisor.
Did you authorize her to sign the document that she forgot to send? How were you damaged? Forgery is more than simply signing another's name.
Under no circumstances should a financial advisor be signing any documents in your name. In particular, if the financial planner is doing this in connection with a "switch" of an investment to an insurance product, or switch between different insurance products, they are violating a litany of FINRA rules. It could well be an honest mistake as well. Hard to tell.
"Take action" is a somewhat vague reference given that we can't tell what happened here. Notwithstanding, the action I would take is move your investments to another financial planner - and soon. If you've suffered real financial harm, get a lawyer.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.