Notifying Agents when Custom Object / Custom Object Field Changes

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I would like to transition our custom fields to custom objects / object fields for easier export/import and to conform with this article suggesting it.

I'm having trouble determining if I can perform an action (currently a business rule) that I need with a custom object - basically when the incident object field is updated to a certain value I would like to notify the agent who is assigned to the incident.

I also have a custom object that is related to the incident (an aggregation relationship, where OracleServiceCloud.Incident is the parent). If I could notify the person assigned to the incident when one of those custom objects is created iff a certain field in that custom object has a particular value, that would also work well - actually I believe it would be even better!