Why it works
Admitting that you are a stranger or that your intent is commercial removes the awkward tension of a sales pitch. This builds trust by lowering the reader's suspicion that you are hiding something.
Example
I am reaching out cold because I think our tool is a perfect fit for your specific challenges, though I know you are busy.
An illustration of the mechanism, not a template. Copied verbatim it stops being persuasion and starts being the pattern everyone else is already sending.
Is your sequence pulling this one?
Paste it in and find out which levers are working, which are missing, and which single zero is capping the whole message.