Is the intention to do the assigned penance required for a valid confession?

To my knowledge, the things necessary for a valid confession are the following: 1. Verbal or interpreted (eg if one is mute) confession of at least all known mortal sins committed since one's last valid confession 2. The words *ego te absolvo* or the semantic equivalent said by the priest with the proper intention (presumed to be habitually held) 3. At least imperfect contrition (sorrow for sin on account of God's just punishments) and a firm purpose of amendment/intention to sin no more on the part of the penitent. The priest assigns a penance to make satisfaction for the temporal debt due to sin, which does not have to be performed in order to receive absolution. So, for instance, if the penitent intends to perform the penance, but is distracted after leaving the confessional, and subsequently forgets to do his penance, his confession is still valid. My question is whether that intention to do penance at the time of confession and absolution is necessary for sacramental validity, that is, whether one who positively intends *not* to do his penance is not forgiven, assuming all the other requirements outlined above are satisfied. Please provide citations from a reputable Catholic source, such as a teaching ministry like Catholic Answers, Ascension Press, Word on Fire, or another, or official church documents if they are available.