How to Use LOGIN - register snippet with ajax ?

var core={
ajax:function(param,callback){
		$.ajax({
			url: 'ajax/',type: 'POST',dataType: 'json',data: param,
			beforeSend: function(data){core.loading.start();},
			success: function(data){ console.log('success'); callback.call(this,data);},
			error:function(jqXHR, textStatus, errorThrown){ console.log(errorThrown); console.log(textStatus); },
			complete: function(data){core.loading.close();}
		});
}

var form=$('#registerform').serializeJSON();
					var data = {'action':'register','component':'login','form':form};
					core.ajax(data,register.callback);

<?php
$sanitizedRequests = $modx->sanitize($_REQUEST); // recommended, will be applied to all $_GET, $_POST, $_COOKIE
$_REQUEST = array();
$_REQUEST = $sanitizedRequests;
$output='';

//this is the processor file name
$procname=$_REQUEST['action'];

//this is what component we are referencing
$comp=$_REQUEST['component'];

//get the processor file with path
$f= $modx->getOption('core_path').'components/'.$comp.'/processors/'.$procname.'.php';
if (file_exists($f)) {
	//include that file so the output of the processor is assigned here
	$output= include $f;
} else {
	$output= 'Action not found: '.$f;
}
//convert the processor output to json format
return $modx->toJSON($output);