Android-Mode doesn't work

Hello all, I tried to get the android-mode working, but unfortunately it won't do it. I downloaded the Android-SDK and updated it with the SDK-Manager right out of processing, but everytime I'm starting processing the following error appears and is keeping being reprinted every few seconds:

Problem inside Devices.list()
java.io.IOException: Cannot run program "adb": CreateProcess error=2, Das System kann die angegebene Datei nicht finden
    at java.lang.ProcessBuilder.start(ProcessBuilder.java:1048)
    at java.lang.Runtime.exec(Runtime.java:620)
    at java.lang.Runtime.exec(Runtime.java:485)
    at processing.app.exec.ProcessHelper.execute(ProcessHelper.java:84)
    at processing.app.exec.ProcessHelper.execute(ProcessHelper.java:64)
    at processing.mode.android.AndroidSDK.runADB(AndroidSDK.java:371)
    at processing.mode.android.Devices.list(Devices.java:292)
    at processing.mode.android.Devices.refresh(Devices.java:239)
    at processing.mode.android.Devices.findMultiple(Devices.java:184)
    at processing.mode.android.AndroidEditor$UpdateDeviceListTask.run(AndroidEditor.java:83)
    at java.util.TimerThread.mainLoop(Timer.java:555)
    at java.util.TimerThread.run(Timer.java:505)
Caused by: java.io.IOException: CreateProcess error=2, Das System kann die angegebene Datei nicht finden
    at java.lang.ProcessImpl.create(Native Method)
    at java.lang.ProcessImpl.<init>(ProcessImpl.java:386)
    at java.lang.ProcessImpl.start(ProcessImpl.java:137)
    at java.lang.ProcessBuilder.start(ProcessBuilder.java:1029)
    ... 11 more

I added the paths to ".../tools" and ".../platform-tools" manually to the System-variable "PATH" on my Windows-10-Machine, rebooted the machine, but the error keeps appearing. What to do?

Thanks for any helpful advice, Christian