Possibility nomination: 1-2 horizontal, 2-3 horizontal, 6th vertical
It is best way to set on 6th vertical.
About this situation, there is very important thing, "Bottom Up".
Let's compare these.
In left picture, green and yellow can link by only 6th column. Particularly yellow can't be linked even if there is yellow on next.
In contrast, right picture, these problems are resolved.
Here is another example.
About left picture, best way is to set on 5th vertical (with limiting death tower).
but red and green are conflicted.
In contrast, right picture, constraint is looser by selecting primis tower.But it means dead of three colors tower. There are advantage and disadvantage.
■Another situasion of bottom-up
Next set, double yellow desires to be set 6th vertical. (Then 1st vertical as auxiliary is better next to 6th vertical.)
This double can't be contained in tower (or contain in 3rd chain recall).
But such bottom-up is better than wasted.
If you want to contain this double yellow on tower, double is set on 5th vertical.
But there is a constrait of color order: green→red→purple→yellow on 4th column.
(As a easy thinking, 4th column is said to desire to be 2 step higher than 5th column. In that picture, 5th column is too high.)