I am "adjective" and I am "present continuous" in one sentence

Do I need to use "I am" twice in one sentence, or it is enough to use it only in the beginning? Where does this rule come from?

My example:

I am fluent in three languages and I am pursuing the XXX designation.

OR

I am fluent in three languages and pursuing the XXX designation.

Solution 1:

I would suggest:

I am fluent in three languages and am pursuing the XXX designation.

because the person "I" is clear, but the "am" is needed to clarify that you are pursuing - is it at of the verb structure, I think.

Solution 2:

If you use only one "am", you are committing syllepsis, forcing a single word to do unexpected double duty within the sentence, in this case first as a linking verb and second as part of the present participle construction.

As @Schroedingers Cat points out, the best way to resolve this is to repeat the "am" but leave the "I" off, as a fairly standard parallel construction.

(See this link for many fine examples of syllepsis.)