Automaton

Some Problems With Modal Logic
I have discovered two major problems with modal logic, and no doubt there are more following similar forms. Anyone care to demolish my half-witted attempt at serious philosophy?

Argument 1 - everything that is possible is actual
1. <>p                        (any logically possible thing)
2. <>p -> <>[]p           (M10 Lewis axiom)
3. <>[]p                     (modus ponens from 1 and 2)
4. <>[]p -> p               (derived from axiom B)
5. p                           (modus ponens from 3 and 4)

Argument 2 - everything that is actual is necessary
1. p                           (any actual thing)
2. p -> <>p                 (H5 or M6 Lewis axiom)
3. <>p                        (modus ponens from 1 and 2)
4. <>p -> <>[]p            (M10 Lewis axiom)
5. <>[]p                       (modus ponens from 3 and 4)
6. <>[]p -> (p -> []p)     (HCR1 axiom)
7. p -> []p                    (modus ponens from 5 and 6)
8. []p                           (modus ponens from 1 and 7)