Is purification valid if one intends to renew purity while being in a state of major impurity (Hadath)?

Primary text

There are two narrations concerning this matter. The first states that the purification is valid because it is a prescribed act of worship, and thus what was intended should be realized, supported by a relevant narration and by analogy to intending the lifting of impurity. The second narration states that the purification is invalid because the person did not intend to lift the impurity or an act encompassing it, making it analogous to intending to cool down.