When do you agree the past participle?

With verbs such as 'aller' and 'venir', the auxiliary verb is être and the past participle needs to agree with the subject.e.g. Il est allé à Paris. Elle est allée à Bruxelles.With most verbs the auxiliary verb is avoir and the past participle does not normally agree.e.g. Elle a mangé la pomme.However, if the direct object (in this case 'la pomme') precedes the verb, then the past participle does have to agree.e.g. Elle l'a mangée or La pomme qu'elle a mangée.Here the past participle agrees with the direct object ('la pomme') not the subject ('elle').e.g. Le fromage qu'elle a mangé or La pomme qu'il a mangée.With reflexive verbs the auxiliary verb is être so the past participle does normally agree.e.g. Il s'est levé. Elle s'est levée.However, if the reflexive verb also has a direct object then the past participle does not agree with the reflexive pronoun.e.g. Elle s'est cassé le bras.Here the reflexive pronoun is treated as an indirect object (think of it as 'She broke her arm of herself.')