maybe think of analyse in simpler terms = as explanation.
the key thing is explaining the importance/impact/affect etc of the evidence you have just mentioned. eg the impact that the CMC had on US Soviet relations and what this meant for the wider context of the Cold War. Explanation is key, you can state as many facts as you want but that wont get you top marks, you need to explain (=analyse) why this fact is included in the essay ie how you can link to the question.
make sure you've talked directly to your teacher as they will know where you are lacking in your analysis therefore you get clarity (also look at written feedback on previous essays, and maybe think about how you would re-write a paragraph). take heart that you can remember evidence, that is super useful, just make sure that the evidence you use is definitely relevant to the essay and your argument, this is where explanation comes in to back up your evidence.
good luck in your exams