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Welfare initiative with intent: right for everyone (8)

Ross

I believe the answer is:

outreach

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'welfare initiative' is the definition.
The definition and answer can be both acts as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'intent right for everyone' is the wordplay.
'intent' becomes 'out' (I can't explain this - if you can you should believe this answer much more).
'right' becomes 'r' (common abbreviation).
'for everyone' becomes 'each' (I've seen this before).
'out'+'r'+'each'='OUTREACH'

'with' is the link.

Can you help me to learn more?

(Other definitions for outreach that I've seen before include "Organisation's influence in the community" , "evangelistic work" , "Involvement with community" , "Missionary activity" , "spreading the message further afield?" .)

I've seen this clue in The Times.
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