Typos and I are friends and have been for years now ;-) but I try not to mis-inform.

I checked with Wordnet 3.0

mediate: Verb

1. act between parties with a view to reconciling differences

2. occupy an intermediate or middle position or form a connecting link or stage between two others

meditate: Verb

1. reflect deeply on a subject

2. think intently and at length, as for spiritual purposes

So I think the words in your post are meditate and contemplate.

Another look?