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Converter Design

Other Parts Discussed in Thread: TPS55288

I have been working on a converter which includes the following specification.
Vin is from Li-ion battery cella ( Vin 9.6V to 12.6V nominal 11.6V )
the output will be 5V@2A, 20V@3A. and I should be able to charge the battery pack with 60W of power.
I am thinking of 4 switch Buck-boost converter but want some expert advice on this design please help me.