You can certainly check the start and status of an Automation using a SSJS Script Activity. If you don't see it in your list of Activity types, SFMC Support can enable it for you.
Here's an example that retrieves and starts an Automation if it's not already running.
<script runat="server">
Platform.Load("Core","1.1.1");
var automationCustomerKey = "CUSTOMERKEY-OF-AUTOMATION"
var rr = Platform.Function.CreateObject("RetrieveRequest");
Platform.Function.SetObjectProperty(rr, "ObjectType", "Automation");
Platform.Function.AddObjectArrayItem(rr, "Properties", "ProgramID");
Platform.Function.AddObjectArrayItem(rr, "Properties", "CustomerKey");
Platform.Function.AddObjectArrayItem(rr, "Properties", "Status");
var sfp = Platform.Function.CreateObject("SimpleFilterPart");
Platform.Function.SetObjectProperty(sfp, "Property", "CustomerKey");
Platform.Function.SetObjectProperty(sfp, "SimpleOperator", "equals");
Platform.Function.AddObjectArrayItem(sfp, "Value", automationCustomerKey);
Platform.Function.SetObjectProperty(rr, "Filter", sfp);
var retrieveStatus = [0,0,0];
var automationResultSet = Platform.Function.InvokeRetrieve(rr, retrieveStatus);
var ObjectID = automationResultSet[0]["ObjectID"];
var Status = automationResultSet[0]["Status"];
if (ObjectID != "null") {
/*
Code Status
-1 Error
0 BuildingError
1 Building
2 Ready
3 Running
4 Paused
5 Stopped
6 Scheduled
7 Awaiting Trigger
8 InactiveTrigger
*/
if (Status == 2) {
var obj = Platform.Function.CreateObject("Automation");
Platform.Function.SetObjectProperty(obj, "ObjectID", ObjectID);
var po = Platform.Function.CreateObject("PerformOptions");
var performResult = [0,0,0];
var performStatus = Platform.Function.InvokePerform(obj, "start", performResult, po);
} else {
// already running
}
} else {
// automation not found
}
</script>
Some additional details here: Retrieving and Starting an Automation with SSJS