I'm using the following to open a new record modal on a custom lwc

this[NavigationMixin.Navigate]({
      type: 'standard__objectPage',
      attributes: {
          objectApiName: this.childObjectApiName,
          actionName: 'new'                
      },
      state : {
          count: '1',
          nooverride: '1',
          useRecordTypeCheck : '1',
          defaultFieldValues: inheritParentString,
          navigationLocation: 'RELATED_LIST'
      }
    });

What I need is after the user saves inside of the popup, to run a function that refreshes my lwc component. Unfortunately, I've found no way to trigger anything after the modal is closed. I've tried listening for platform events, appending  .then(result => {}) to the end of the navgation mixin function, but all have failed miserably, and I have lost all hope. Does anyone have any ideas I how to accomplish this? Please help..