When do I agree the past participle when using the passé composé?

When I say agreement, I mean the addition of an 'e' (for gender) and/or an 's' (for number) to the past participle so that it corresponds with the subject or object of the verb. For all verbs that take être as their auxiliary in the past tense, it is necessary to add the agreement for gender and/or number. For example, I am female, so I would have to add an 'e' to the past participle allé, because I am a female subject. So the correct sentence would be 'je suis allée'. If I went with a group of my female friends, the subject would be plural, so it would be necessary to add an 's' as well, to make it 'nous sommes allées'. Luckily, you don't have to add the agreements to the past participles of the verbs which take avoir. So even though I'm female, I wouldn't write 'je suis faite', for example. The only time you agree if it takes avoir is if the direct object of the verb comes before the verb. For example, 'ses parents l'ont gatée', her parents spoiled her. The 'her' - the 'l' - is a feminine object, and comes before the verb: 'ont.', so we add the 'e' to the past participle. If there were multiple daughters, you would add an 's' too. This rule is known as the 'preceding direct object' rule: if the direct object precedes (comes before) the verb, agree the past participle.