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I'm interested in planning and how one is able to take action and plan ahead at the same time. I could imagine one could make observations and project these into the future using past experiences. The reward system could then sort out favorable outcomes which one could aim for, taking the necessary steps.

However I don't know if this is really how the reward system works (I wasn't able to find resources especially for "future" reward) and I can also see difficulties in terms of interference with control of the current situation - planning would have to be handled as some sort of suppressed action.

So are there already cognitive models that try to explain planning and how planning and action could work in parallel (although interacting)?

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Reward systems are one of the most actively studied topics in (cognitive) neuroscience and prediction error - that is, deviations from expected "future" reward - play a big role in that. Since you're particularly interested in models, I recommend checking out the work of Matt Botvinick and Nathaniel Daw. Here are a few papers that might be good starting points:

Glascher, Daw, Dayan, & O’Doherty (2010). States versus Rewards: Dissociable Neural Prediction Error Signals Underlying Model-Based and Model-Free Reinforcement Learning. Neuron, 66, 585-595.

den Ouden, Friston, Daw, McIntosh, & Stephan (2009). A Dual Role for Prediction Error in Associative Learning. Cerebral Cortex, 19, 1175-1185.

Solway & Botvinick (2012). Goal-directed decision making as probabilistic inference: A computational framework and potential neural correlates. Psycholological Review, 119, 120-154.

Botvinick & Plaut (2004). Doing without schema hierarchies: A recurrent connectionist approach to routine sequential action and its pathologies. Psychological Review, 111, 395-429.

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