Automated Outreach Software for Recruiters

As a recruiter, a significant part of my work involves identifying suitable talent and reaching out to them on LinkedIn. Unfortunately, the response rate to these messages is often quite low. I’m considering automating the initial phase of this process: taking a job description, finding matching candidates on LinkedIn, and sending them an automated message.

I only wish to engage further once a candidate responds. Is there any software available that can assist with this?