Dwell: to brood; think moodily or anxiously about something.
Solve: puzzle out; find the solution to (a problem or question) or understand the meaning of.
Planning: thinking, thought, thought process, cerebration, intellection, mentation -- (the process of using your mind to consider something carefully.)
Plan: a series of steps to be carried out or goals to be accomplished.

While I find the definitions somewhat enlightening, I think the difference between dwelling and solving is intent. Dwelling is not intended to accomplish anything positive.

Ultimately, the Serenity Prayer seems to elucidate:

God grant me the serenity
to accept the things I cannot change;
courage to change the things I can;
and wisdom to know the difference.
Living one day at a time;
Enjoying one moment at a time;
Accepting hardships as the pathway to peace;
Taking, as He did, this sinful world
as it is, not as I would have it;
Trusting that He will make all things right
if I surrender to His Will;
That I may be reasonably happy in this life
and supremely happy with Him
Forever in the next.
Amen.

--Reinhold Niebuhr