tsumori/to omou/kangaeru - Intentions behind their use?

I've learnt a number of ways to express my intentions/thoughts, but I'm not 100 percent sure about when to use them. Can someone check the following four sentences and see if I've translated them correctly (please also correct grammar if I've erred...) and have understood their use correctly? And if I haven't could it be explained why?

1. 明日、猫を買います - Straightfoward statement - 'Tomorrow I will buy a cat'

2. 明日、猫を買うと思います - I've seen a cute cat and think *squeeeeeeee* cute! Owning a cat would be fun! So I say 'Tomorrow, I think I'll buy a cat'

3. 明日、猫を買うつもりだ - I want a cat and therefore - 'Tomorrow, my intention is to buy a cat'

4. 明日、猫を買うと考えます - I've wanted a cat for a while, maybe bought some cat things in preperation - 'Tomorrow, I plan to buy a cat'

I'm not really sure about 4, as my teacher informed me that kangaeru is more 'plan', although I see it tranlated in example sentences at jisho.org as 'think'

I'm REALLY not sure about 3. What circumstances would I use 3 and not 2 or 4?

And my teacher explained that to omou is used more in regard to feelings, so have I gotten my use correct in 2?

Obviously major confusion for me here! Any help greatly appreciated!

Let's back up a big step; 今日 is "today".

Whoops！ Hurriedly typing through lunch break. Okay for 今日、read 明日…

つもり expresses an obvious intention to buy it, whereas 思う expresses the speaker's diffidence. 考える is hardly used with verbs that express the speaker's volitional action like 買う. #4 sounds like that the speaker is talking about third person's action(buying a cat) to me.

Thank you!
So 3 is that I definitely want to buy a cat, and I shouldn't use 4 in such examples with myself as the subject.

When you say 2 (と思い) indicates my diffidence, is this similar to the use of でしょう to soften sentences? We were always informed it was a just a way of expressing our personal opinion, and we could use 多分 or きっと to modify how sure we were about what we think. Does it always express diffidence when used? Or depends on context? If I'm referring to an action to be carried out I should use つもり not と思い to express firmly that I'm going to do it?

つもり always expresses stronger intention than ～と思う, even with きっと.
There are several expressions to show the degree of intention, e.g., 買おうと思う/思っている, 買いたいと思う/思っている, 買おうと考えている/買おうかと考えている,,,. Among these expressions, 買おうと思っている is relatively close to 買うつもりだ. So, it's not just the problem of the difference among つもりだ, 思う and 考える.

Toritoribe said:

Among these expressions, 買おうと思っている is relatively close to 買うつもりだ. So, it's not just the problem of the difference among つもりだ, 思う and 考える.

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I understood 買うつもりだ to carry a stronger sense of determination than 買おうと思っている. The crucial difference with 買おうと思っている being that 買おうと思っている can focus on more ambiguous, less definite situations, for example expressing an on the spot decision rather than a predetermined conviction to follow through on the desired outcome.

予定 is another possibility but translated better as "plan to" and I suppose carries the unique implication that not only has the speaker decided to want to do something, but has taken actual concrete steps on the way to achieving that goal. :?