The specific cause of action, if the court agrees to file a case, shall be decided by the judge of the filing court. Your situation is generally a contract dispute.
As for whether it is possible to prosecute by agreement, it is possible in law or theory. However, in practice, please prepare some evidence of the other party's breach of contract and the identity certificates of both parties, that is, who is the plaintiff and who is the defendant. If the defendant is a company, go to the industrial and commercial bureau to pull the basic information. Then prepare the complaint. There are other procedural things that the court will let you fill out.