"can" isn't really a proper verb. It's a "modal auxiliar" and as such has no infinitive form, which is what is called for in your first example, nor does it have a participial form, which is what is called for in the second. You might think of "can" as a special shortcut for the present tense of "be able to": "I am able to do it = I can do it". But it won't work, for example, in the future tenses because these call for infinitive forms. "I will be able to do it" or "I am going to be able to do it" have no corresponding "can" constructions, though the use of "can" can have a future sense: "I can do it tomorrow".
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