Pyramiding vs Selling into Strength

Pat, I really appreciate all the things I'm learning here - and I have a question regarding Pyramiding into a position and how you can be doing that at the same time as you are selling into strength as it sounds like a contradiction to be buying in (pyramid, 50-30-20) and yet selling into strength (usually 20%-25% sells).
I know one reason you sell is to take a profit on the shares you sell to lessen risk, but if you are pyramiding in, then when you buy the shares back, you now bought shares at a higher cost-basis than what you previously had.
Can you explain if you do this:
Are you doing buying and selling in conjunction, or only doing one or the other (I know it depends on market conditions, set-up, charts).
Do you mind raising your average cost by buying new shares? - as each new buy could essentially be treated as a "new position" (and also have its own separate stop loss).
Also, I guess the sells into strength help take profit off the table which increases your overall account size - thus allowing you eventually buy more stocks/positions even if they end up being a higher price - because it will still be governed by your stops or sells.
Thank you for answering all this helping us learn.