Mongoose separate documents while embedding schema?

I would like to save a document _id to another schema's array after a user creates a new document. In short: a user saves a video URL, and I would like to save the video's document _id to an array in the user schema. I am having trouble figuring out how to do this. Here are my model files:

videos.js:

// Video Model
// -------------

var mongoose = require('mongoose');
var Schema = mongoose.Schema;

// Embedded document schema
var NotesSchema = new Schema({
    timecode  : String,
    text      : String
});

// Main schema
var VideoSchema = new Schema({
    title   : String,
    url_id  : String,
    notes   : [NotesSchema]
});

module.exports = mongoose.model('Note', NotesSchema);
module.exports = mongoose.model('Video', VideoSchema);

account.js:

// Account Model
// -------------

var mongoose = require('mongoose');
var Schema = mongoose.Schema;
var Video = require('../models/videos.js');
var passportLocalMongoose = require('../node_modules/passport-local-mongoose/lib/passport-local-mongoose.js');

var AccountSchema = new Schema({
    username: String,
    salt: { type: String, required: true },
    hash: { type: String, required: true },
    videos: [VideoSchema]  // <- need to save here
});

AccountSchema.plugin(passportLocalMongoose);

module.exports = mongoose.model('Account', AccountSchema);

Here's how I currently have the code setup to create a document and save to MongoDB.

var video = new Video({
    title   : req.body.title,
    url_id  : req.body.url_id
});

video.save(function(err) {
    if (err) {
        console.log(err);
    } else {
        res.redirect('videos/' + video._id);
        console.log('video saved.');
        console.log('video information: ' + video);
    }
});

Basically I don't understand how to save to video and only send the video document _id to the array in the account schema. How do I do this?

EDIT:

Despite implementing the suggested fixes, data._id is not saving to the array inside the Account schema. No error is thrown. When I check on a account using the mongo CLI, the array is empty.

Here are my current changes:

video.js

// Video Model
// -------------

var mongoose = require('mongoose');
var Schema = mongoose.Schema;

var NotesSchema = new Schema({
  timecode  : String,
  text      : String
});

var VideoSchema = new Schema({
  title   : String,
  url_id  : String,
  notes   : [NotesSchema]
});

module.exports = mongoose.model('Note', NotesSchema);
module.exports = mongoose.model('Video', VideoSchema);

account.js

// Account Model
// -------------

var mongoose = require('mongoose');
var Schema = mongoose.Schema;
var Video = require('../models/videos');
var passportLocalMongoose = require('../node_modules/passport-local-mongoose/lib/passport-local-mongoose.js');

var AccountSchema = new Schema({
    nickname: String,
    birthday: Date,
    videos: [{ type: Schema.Types.ObjectId, ref: 'Video' }]
});

AccountSchema.plugin(passportLocalMongoose);

module.exports = mongoose.model('Account', AccountSchema);

video-route.js

var util = require('util');
var mongoose = require('mongoose');
var Video = require('../models/videos');
var Account = require('../models/account');

var video = new Video({
  title   : req.body.title,
  url_id  : goodVimeoId
});

video.save(function(err, data) {
  if (err) {
    console.log(err);
  } else {
    Account.findOne({username : req.user.username}, function(err, result) {
      result.videos.push(video._id);
      res.redirect('videos/' + video._id);
    });

  }
});

Any suggestions on why the video data is not saving to the account? Thanks again.