As the saying goes, if you want something done, do it yourself. This is true especially when you are working solo. Who else is going to do it? The best person to rely on is yourself.
But this also applies in a team setting where it is always better to do it yourself first. Everyone in the team has their own responsibility and you should hold up your end of the bargain.
Of course, it is okay to seek assistance. That is why we work in teams. We need the strength of others to overcome ever greater challenges. We should never be afraid to ask for help. It is not a sign of weakness but a sign of humility.
It might seem paradoxical to be self-reliance and seek assistance of others at the same time. The first lesson is to realize that you need to do your very best if you want something done well. The other is to admit that you can't do everything yourself and it's okay to get some help in achieving your goals.