Prepopulate a Field via Button override of Clone button

Question

I need to prepopulate the Cloned_From__c field on the case when a user clicks the standard clone button, the field should be the case that is being cloned. How do I prefill this field out before I click save after clicking clone?

Here is what I have....

public with sharing class CloneClosedCaseOverrideController {
    private ApexPages.StandardController standardController {get; set;}
    public Case CaseRecord{get;set;}
    public CloneClosedCaseOverrideController(ApexPages.StandardController standardController){
        this.standardController = standardController;
        CaseRecord = (Case)standardController.getRecord();

    }
    public PageReference cloneCase(){
        Case CaseCloned;
        try{
            CaseCloned = CaseRecord.clone(false, false, false, false);
            CaseCloned.Cloned_From__c = CaseRecord.Id;
            insert CaseCloned;
        } catch (Exception e){
            ApexPages.addMessages(e);
            return null;
        }
        return new PageReference('/'+CaseCloned.Id);
    }
}

Here is the VF

<apex:page standardController="Case" extensions="CloneClosedCaseOverrideController"
           action="{!cloneCase}">
    <apex:pageMessages />
</apex:page>

Feel like I am close here...Thanks in advance!

Edit: I added some visual here...

Here I want this view to still pop up and have a the cloned from field filled out. So I want this view even when I do a override