C++ Class inheriting from template class without knowing the type?

I am designing a template class Policy which needs to be able to handle pointers to other classes.

template <class P>
class Policy
{
  private:   
    const P *state;
  public:
    Policy (P const* s) : state(s){};
};

This works fine. Now I want to inherit from the above template class and create new subclasses:

class Greedy : public Policy<???>
{
  public:
    template <typename P> Greedy (P const* s) : Policy(s) {}:
};

class Explora : public Policy<???>
{ 
  public:
    template <typename P> Explora (P const* s) : Policy(s) {}:
};

Problem is that when defining those classes I do not know what type they will be using for the base template class. Is this even possible to do ? I want the type obtained from the inherited class constructor (probably templated), and then pass it to the base class construtor. Can I do that ? If yes, how ? typedefining enums ? I have seen this question but it doesn't in my opinion really answer the question.