I am trying to use the following struct as a custom key for std::map:
struct ActionId {
        // ENCAPSULATED MEMBERS
    private:
        size_t _id;
        static size_t _root;
        static size_t incrementedRoot() {
            return (_root += 1);
        }
        // INTERFACE
    public:
        ActionId() :
            _id(incrementedRoot()) { }
        ActionId(const ActionId& that) :
            _id(that._id) { }
        ActionId& operator=(const ActionId& that) {
            this->_id = that._id;
            return *this;
        }
        bool operator==(const ActionId& that) const {
            return this->_id == that._id;
        }
        bool operator!=(const ActionId& that) const {
            return this->_id != that._id;
        }
        bool operator<(const ActionId& that) const {
            return this->_id < that._id;
        } 
};
The following dictionary is a member of a separate InputManager class:
std::map<ActionId, std::set<sf::Keyboard::Key>> _keyBindings;
which is accessed in this member function:
std::set<sf::Keyboard::Key> InputManager::keysBoundTo(ActionId action) const {
    return _keyBindings[action];
}
Unfortunately, the function is throwing this compiler error:
error C2678: binary '[' : no operator found which takes a left-hand operand of type '
const std::map<Game2D::ActionId,std::set<sf::Keyboard::Key,std::less<_Kty>,std::allocator<_Kty>>,std::less<Game2D::ActionId>,std::allocator<std::pair<const Game2D::ActionId,_Ty>>>' (or there is no acceptable conversion)
According to this article, the operator<() member of ActionId with const qualification should be sufficient to make it a custom map key, while this article says that all I need is to make ActionId copiable and assignable.  Clearly, my struct meets both of these criteria, so why won't InputManager::keysBoundTo() compile?