Crossword Genius

I'm aching running round lake (8)

Ross

I believe the answer is:

michigan

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

'i'm aching running' is the wordplay.
'running' is an anagram indicator.
'im'+'aching'='imaching'
'imaching' is an anagram of 'MICHIGAN'.

Can you help me to learn more?

(Other definitions for michigan that I've seen before include "US Great Lakes state" , "State of Detroit" , "I'm aching to see American state" , "US state and Great Lake" , "I'm aching to go to a Great Lake" .)

I've seen this clue in The Telegraph.
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