How can I alter a MenuItem on the Options Menu on Android?

I have an Options Menu on my Activity with an MenuItem "Start". When this MenuItem is selected I would like to alter the Menu so it contains a MenuItem "Stop". And finally when "Stop" is selected, I would like to alter back to "Start".

Here is parts of my code that isn't working. I have both "Start" and "Stop" listed in mymenu.xml I should probably remove "stop" when the menu is created:

public class MyActivity extends Activity {
    private boolean isStarted = false;

    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        MenuInflater inflater = getMenuInflater();
        menu.removeItem(R.id.stop);
        inflater.inflate(R.menu.mymenu, menu);
        return true;
    }

    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        switch (item.getItemId()) {
        case R.id.start:
            isStarted = true;
            return true;
        case R.id.stop:
            isStarted = false;
            return true;
        default:
            return super.onOptionsItemSelected(item);
        }
    }

    @Override
    public boolean onPrepareOptionsMenu(Menu menu) {
        if(isStarted) {
            menu.removeItem(R.id.start);
            menu.add(R.id.stop);
        } else {
            menu.removeItem(R.id.stop);
            menu.add(R.id.start);
        }
        return true;
    }
}

For this type of operation I usually choose not to alter the menu items, but just hide the ones you don't need:

@Override
public boolean onPrepareOptionsMenu(Menu menu) {
    super.onPrepareOptionsMenu(menu);
    menu.findItem(R.id.start).setVisible(!isStarted);
    menu.findItem(R.id.stop).setVisible(isStarted);
    return true;
}