Crossword Genius

Race around 500 trees without thinking (9)

Ross

I believe the answer is:

headfirst

I'm a little stuck... Click here to teach me more about this clue!

'without thinking' is the definition.
(I've seen this before)

'race around 500 trees' is the wordplay.
I cannot quite see how this works, but
'500' could be 'd' (Roman numeral for 500) and 'd' is found within the answer.
'trees' could be 'firs' (fir is a kind of tree) and 'firs' is found within the answer.
'race' could be 'heat' (I've seen this before) and 'heat' is located in the leftover letters.
This accounts for all the letters.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for headfirst that I've seen before include "Without thinking" , "If trashed, dive as divers usually do" , "Impetuously" , "rashly" .)

I've seen this clue in The Telegraph.
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