As far as my understanding goes, Hensels Lemma is used on polyonmials over the $p$-adic numbers, to calculate its roots iteratively.
There is also the Newton Polygon, which gives us information about the valuation of a root of a polynomial over the $p$-adic numbers. My question is now if there also exists the Newton Puiseux algorithm for $p$-adic numbers and what its difference is compared to Hensels Lemma itself.