<aura:component controller="MyController" implements="flexipage:availableForAllPageTypes,force:hasRecordId" access="global">
    <aura:attribute name="recordId" type="Id"/>
    ...
    <button type="button" onclick="{!c.doRun}">Activate Next</button>
</aura:component>

<apex:page standardController="CustomObject__c">
    <apex:includeLightning />

    <div id="mydiv" />

    <script>
    $Lightning.use("myApp", function() {
        $Lightning.createComponent("myComponent",
                                   { recordId : "{!CustomObject__c.Id}" },
                                   "mydiv",
                                   function(cmp) {});
    });
    </script>
</apex:page>

({doRun : function(component, event, helper) {
    var action = component.get("c.run");

    action.setCallback(this, function(response) {
        if (component.isValid() && response.getState() === "SUCCESS") {
            $A.get("e.force:refreshView").fire();
        }
    });

    $A.enqueueAction(action);
}})