I have written the letter.
Personally, I prefer Michael Lewis's suggestions: first form for the base, bare-infinitive, dictionary-entry form; second form for the Past Simple form; and third form for the 'past partciple'. I also like ING-form for the 'present participle' and 'gerund'. This does away with any confusion that is caused by using tense/time-words such as past and present, or by such technical terms as gerund and participle. However, at present the traditional names hold sway in most published materials, and our students and colleagues may be very familiar with them. We ignore them at our peril.