As per the comments, invoking an Action from the view but as part of the Invoke Application phase can be done with the help of omnifaces' InvokeActionEventListener:
<f:metadata>
<f:event type="postInvokeAction" listener="#{bean.action}" />
</f:metadata>
When deploying with JSF-2.2 you could also use:
<f:metadata>
<f:viewAction action="#{bean.action}" />
</f:metadata>