Calculating a "flag" based on two images and add it as a new band in Google Earth Engine

In following script, I used a dem image imported from my assets where I arbitrarily assigned a threshold of 2000 m for separating high and low areas. These images (high1 and low1) were used to create a new image that has a band with a flag for low and high areas (with values of 10 and 100; respectively).

var image = ee.Image("users/joseguerreroa/raster_files_utah/utah_demUTM12");

var imageVisParam = {"opacity":1,"bands":["b1"],"min":1366,"max":3397,"gamma":1};

print(image);

var bounds = ee.Geometry.Polygon(ee.Geometry(image.get('system:footprint'))
  .coordinates());

Map.addLayer(image, imageVisParam, 'image');
Map.centerObject(image);

var minValue = image.rename('min')
  .reduceRegion(ee.Reducer.min(), bounds);

print("min", minValue.get('min'));

var maxValue = image.rename('max')
  .reduceRegion(ee.Reducer.max(), bounds);

print("max", maxValue.get('max'));

var high1 = image.gt(2000).multiply(100).rename('high area').selfMask();

var imageVisParam2 = {"opacity":1,"bands":["high area"],"palette":["0c08ff"]};

Map.addLayer(high1, imageVisParam2);

var low1 = image.lte(2000).multiply(10).rename('low area').selfMask();

var imageVisParam3 = {"opacity":1,"bands":["low area"],"palette":["orange"]};

Map.addLayer(low1, imageVisParam3);

var new_image = low1.addBands(high1);

var imageVisParam4 = {"opacity":1,"bands":["low area"],"palette":["red"]};

Map.addLayer(new_image, imageVisParam4);

var imageVisParam5 = {"opacity":1,"bands":["high area"],"palette":["green"]};

Map.addLayer(new_image, imageVisParam5);

print(new_image);

After running above script in GEE console editor, it can be observed as follow that new image has two bands (low and high area) as expected.