Get a Stirrup Hoe. It has a stirrup shaped blade that roots up grass when you 'rake' with it. It works great (I had to use one for three hours today at a nursery). After you get all the big clumps/dead stuff up, you can spread a couple inches of composted manure over your yard (composted manure looks like dirt and doesn't smell) and reseed.
Then use Scotts Turf Builder.
Plant a couple trees (tough ones like maples). They should do fine in the clay as long as you stake them out and water them enough until they can establish roots.
I don't think it is worth you while to mess with the clay. It will just bog you
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"Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill
"All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence
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