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The phrase "within their reach" is correct and can be used in written English.
It is typically used to describe something that is attainable or accessible to someone. Example: With hard work and determination, success is within their reach.
Exact(60)
But that power is within their reach.
If those concerned prefer aggression then it's within their reach.
ChildLine can be the only lifeline within their reach.
The last eight should be well within their reach.
"You look at the guys we have, it's within their reach".
With Australia's powerful batting line-up that target appeared well within their reach.
With Dravid, Ganguly and Tendulkar in the ranks, that should be well within their reach.
Politicians can't be blamed for tinkering; the levers are within their reach.
For example, unsupervised children may choke on small objects that have been within their reach.
None of these objectives were politically within their reach, however, given the makeup of the bench.
Someone had to put that critical first job within their reach.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com