Beliefs belong in church, they have nothing to do with rational thought.
Regarding your admitted carelessness, welcome to the real world.
Part of Ayn Rand's brilliance is that she continually checked her premises. In so doing, she used her mind to check on her mental processes, a self-exam far superior to Christians checking their consciences over adherence to things like man-made religious rules. Checking her premises was also a habit that resulted in her writing with incredible clarity -- always.
You are describing an impossible computer loop - where a computer thinking about its thinking discovers truth. In your worldview, a computer could develop 'morality.' Rand is exactly the same. She purports to develop morality through reason, but actually uses her underlying morality and reason to come up with a more defined version of her underlying morality. Her primary claim is bogus.