scheduling runnable tasks in java

I am following up an interesting question on so, on usage of ScheduledThreadPoolExecutor for some repeating task.

Scheduling this object returns a ScheduledFuture object which one can use to cancel the next run of the task.

One thing to note here is the task itself is completely decoupled from the schedule--

ScheduledExecutorService executor = new ScheduledThreadPoolExecutor(1);
ScheduledFuture nextSchedule = 
    executor.schedule(task, 60000, TimeUnit.MILLISECONDS);

where-

SomeTask task = new SomeTask();

So the task itself is not aware of the schedule. Please enlighten if there is a way to get the task to cancel and create a new schedule for itself.

Thanks