petition arrived from court, can I cross petition?

Hi all,
I received the divorce petition from the court today and its the same as the one my stbx sol sent and I disagreed with it all as it is full of lies, I asked that it be changed and also corrected as my stbx listed her 23yr old son on the D8 and he has not lived at the FMH in over 3 years.
It is on the grounds of my unreasonable behaviour and she also wants me to pay the costs.
I have since found out that the whole divorce appears to have been orchestrated and that she has been seeing another man, i dont have any proof of this being a sexual relationship but im sure it is, shall I just file a cross petition under her adultery or just sign the papers and leave it at that?

any help would be much appreciated as im so lost and alone and not sure whether to fight or just give in.

Cross petitioning will only cost money.

Why not just put that you accept the marriage is over but disagree with the facts as stated and reserve the right to dispute them?

Unless you get an admission of adultery or can produce a child resulting from it or some very pornographic pictures you''re wasting your time and money. End result is the same at the end of the day anyway whoever petitions for the divorce.