One play button to play multiple movie clips sequentially

I have 4 movie clips on the stage that are played by themselves with their own play button. I need to get a separate play button (top right corner on linked files) to play all the separate movie clips in sequential order without messing up their individual playback. I can't find anything on how to write that script so that button currently doesn't work. I'm not sure where to start with the code, any ideas? I'm pretty novice at this so specifics are appreciated.

TESTING multi play btns_9.fla - Google Drive

TESTING multi play btns_9.swf - Google Drive

Here is the current AS for the other 4 movie clips:

var playing:Boolean = false;

function stopAllCounts():void {

     Count1.gotoAndStop(1);

     Count2.gotoAndStop(1);

     Count3.gotoAndStop(1);

     Count4.gotoAndStop(1);

}

/*1st movieclip*/

Count1.stop();

function startCount1(event:MouseEvent):void {

     var stopped:Boolean = Count1.currentFrame == 1 || Count1.currentFrame == Count1.totalFrames;

     stopAllCounts();

     if (stopped) {

          Count1.gotoAndPlay(1);

     }

}

startButton1.addEventListener(MouseEvent.CLICK, startCount1);

/*2nd movieclip*/

Count2.stop();

function startCount2(event:MouseEvent):void {

     var stopped:Boolean = Count2.currentFrame == 1 || Count2.currentFrame == Count2.totalFrames;

     stopAllCounts();

     if (stopped) {

          Count2.gotoAndPlay(1);

     }

}

startButton2.addEventListener(MouseEvent.CLICK, startCount2);

stop();

/*3nd movieclip*/

Count3.stop();

function startCount3(event:MouseEvent):void {

     var stopped:Boolean = Count3.currentFrame == 1 || Count3.currentFrame == Count3.totalFrames;

     stopAllCounts();

     if (stopped) {

          Count3.gotoAndPlay(1);

     }

}

startButton3.addEventListener(MouseEvent.CLICK, startCount3);

stop();

/*4th movieclip*/

Count4.stop();

function startCount4(event:MouseEvent):void {

     var stopped:Boolean = Count4.currentFrame == 1 || Count4.currentFrame == Count4.totalFrames;

     stopAllCounts();

     if (stopped) {

          Count4.gotoAndPlay(1);

     }

}

startButton4.addEventListener(MouseEvent.CLICK, startCount4);

stop();