Write a 5-6 page paper in answer the following prompt. Do not write more than 6

Write a 5-6 page paper in answer the following prompt. Do not write more than 6 pages. Papers should be double-spaced, written in Times New Roman 12, with one inch margins. Please note the suggested length for each part of the prompt below. You should also have an introductory paragraph with a thesis (a thesis that corresponds to the third part of the prompt).
Prompt
Kant asks how synthetic a priori propositions are possible. First, explain the distinction between a priori and a posteriori knowledge and between analytic and synthetic propositions. Then also discuss why synthetic a priori knowledge seems, on the face of it, to be unattainable (roughly one page). Second, answer one of the following two questions: either a) how are the synthetic a priori propositions of mathematics possible?; or b) how are the synthetic a priori propositions of natural science possible? Then also criticize some aspect of Kant’s answer and offer a response on Kant’s behalf. In other words, pick either part one or part two of the transcendental problem and discuss and criticize either Kant’s views on mathematics and the forms of our sensibility (focus on geometry and space) or his views on natural science and the concepts of our understanding (focus on causation) (roughly two pages). Third, answer the following question: how, if at all, are the synthetic a priori propositions of metaphysics possible? Then also criticize some aspect of Kant’s answer and offer a response on Kant’s behalf (roughly two pages).
Assessment
Assessment of papers will be based on the following criteria (not listed in order of importance): a) mastery of the course materials (concepts, arguments, etc.); b) clear thesis & sound argumentation; c) clarity of expression & meaningful structure; d) originality & thoughtfulness.