the intention is something formed in the heart, not what is uttered on the tongue, and none except you and Allah (swt) know what is in your heart.
There are some sufi sects who claim that thier scholars or peers know the matter of the heart, but this is a statement of shirk.
So your intention is what ever you intend in your heart.
It is sufficient to think "I want to do such and such"
I think the questioner knows better than the ones being asked how to tell if your intention is sincere, seeing that others dont know your intention let alone the sincerity of the intention.
Even the messenger of Allah (pbuh) did not know peoples intention until Jibreel (as) revealed it to him.
Hence the famous hadith narrated by Umar
I heard Allah's Apostle saying, "The reward of deeds depends upon the intentions and every person will get the reward according to what he has intended. So whoever emigrated for worldly benefits or for a woman to marry, his emigration was for what he emigrated for."
Sahih Bukhari Volume 1, Book 1, Number 1: