Trying to read serial data being printed by an Arduino using Processing

Alright, so following your suggestions I've modified my two sets of code. The problem I'm having now is that Processing is not receiving the data. My code creates a nice text file in the sketch directory, but the text file is empty. I think it's a problem with how I'm printing my BPM, but I can't be sure whether I've set up Processing correctly in order to receive data. Any help would be appreciated!

New Processing code:

import processing.serial.*;
Serial port; 
PrintWriter output;

int BPM;         // HOLDS HEART RATE VALUE FROM ARDUINO


void setup() {
  // Create a new file in the sketch directory
  output = createWriter("BPM.txt"); 
  
  
  // GO FIND THE ARDUINO
  println(Serial.list());    // print a list of available serial ports
  // choose the number between the [] that is connected to the Arduino
  port = new Serial(this, Serial.list()[1], 115200);  // make sure Arduino is talking serial at this baud rate
  port.bufferUntil('\n');  // set buffer full flag on receipt of carriage return
}


void serialEvent(Serial port){ 
   String inData = port.readStringUntil('\n');
   inData = trim(inData);                 // cut off white space (carriage return)
   
     BPM = int(inData);                   // convert the string to usable int
//     port.write(1);                     // Try to write to serial port to test if Processing can communicate with correct serial port
   }


void draw() {      // Could use void loop() here instead?
  output.println(BPM);  // Write the BPM to the file
  
}

void keyPressed() {
  output.flush();  // Writes the remaining data to the file
  output.close();  // Finishes the file
  exit();  // Stops the program
}]

The only part of the old Arduino code that I modified was this part (the void loop()):

void loop(){
//  sendDataToProcessing('S', Signal);     // send Processing the raw Pulse Sensor data
//  if (QS == true){                       // Quantified Self flag is true when arduino finds a heartbeat
//        fadeRate = 255;                  // Set 'fadeRate' Variable to 255 to fade LED with pulse
//        sendDataToProcessing('B',BPM);   // send heart rate with a 'B' prefix
//        sendDataToProcessing('Q',IBI);   // send time between beats with a 'Q' prefix
//        QS = false;                      // reset the Quantified Self flag for next time    
//     }
//  
//  ledFadeToBeat();

//sendDataToProcessing('B', BPM);     // send Processing the raw Pulse Sensor data

Serial.println(BPM);  //  Trying again to print to Serial
  
  delay(100);                             //  take a break
}