Produce a single image from an ImageCollection which will have pixel values of the day of the year in which the NDVI had its maximum value

  google-earth-engine, javascript

I am working in Google Earth Engine.
I have an ImageCollection of images for the year 2019.
I have created the NDVI band in the bands List for every image.
I want to produce a single image from the images of my ImageCollection which will have pixel values of the day of the year in which the NDVI had its maximum value.
I have converted the DATE_ACQUIRED of a single image of my ImageCollection to day of the year format with the following script:

// Get a specific metadata property
var date_acquired = image.get('DATE_ACQUIRED');
print('DATE_ACQUIRED:', date_acquired);

var datetime = ee.Date(date_acquired); // Defaults to UTC
var doy = datetime.format('DDD')

print(doy);

and i have created a feature with this script:

// Create a Feature from the Geometry
var DOY = ee.Feature(doy);

My thought is to insert the DOY property in every image of the ImageCollection and then create the single image which will have pixel values of the day of the year in which the NDVI had its maximum value.
I’m stuck in this and i can not find a solution. Does anyone know how to do this?

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