Are you sure it’s correct that "approach to" should be followed by “doing” and not “do”? Who told you that”? I assume you are just using the verb “do” as an example, but are talking about any verb that might follow “approach to”. Is that correct?
In the following examples ( from https://en.oxforddictionaries.com/definition/approach )
the verb following “approach to” is not using the -ing form:
‘Load management is a systematic approach to control the operation of electrical equipment.’
‘The design and methods are a reasonable approach to study the association between modifiable risk factors and injury from car crashes.’
December 6, 2016
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