Uncheck a CheckBox when a RadioButton is selected

I am dealing with a WiX installer.

I have this CheckBox control:

<Control Type="CheckBox" Id="OfficePluginsEnabledCheckbox" Width="107" Height="17" X="11" Y="114" Text="Enable Installed Add-ins" Property="OFFICEPLUGINSENABLED" CheckBoxValue="1"/>

I have this RadioButtonGroup control:

<Control Type="RadioButtonGroup" Property="INSTALLADDINKEYS" Id="AddinKeysRadioButtonGroup" Width="74" Height="45" X="218" Y="131">
    <RadioButtonGroup Property="INSTALLADDINKEYS">
      <RadioButton Text="All Users" Height="17" Value="AllUsers" Width="200" X="0" Y="0" />
      <RadioButton Text="Current User" Height="17" Value="CurrentUser" Width="200" X="0" Y="15" />
      <RadioButton Text="None" Height="17" Value="None" Width="200" X="0" Y="30" />
    </RadioButtonGroup>
    <Publish Property="OFFICEPLUGINSENABLED"><![CDATA[INSTALLADDINKEYS="None"]]></Publish>
</Control>

I am trying to de-select the CheckBox when None is selected as the RadioButtonGroup's RadioButton by publishing the OFFICEPLUGINSENABLED property to the check box. However this does not work as OFFICEPLUGINSENABLED is not published. Why is this, and how can I fix it?