Is there a how-to to prove reincarnation?
And secondly, I would like to lessen bad action from the previous life. And how do I do that?
You are confusing belief or faith with a hypothesis.
Instead of a methodological answer, this question might, perhaps arguably, be tackled better from a slightly more philosophical angle. Let's go through the relevant terminologies.
An acceptance that something exists or is true, especially one without proof.
A related term is faith
[F]irm belief in something [often in a religious context] for which there is no proof
Indeed Reincarnation is a
[An] idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world.
Reincarnation has not been observed in the natural world. Instead, it is based on faith in religious belief.