[ExI] Intermittent liar puzzle #3

[Adrian Tymes]

Since I've answered the others, figured I might as
well contribute one of my own.

Jamal's religion requires him to lie to outsiders on
one specific day of each year, and tell the truth to
outsiders at all other times.  You are an outsider,
and you do not know what his schedule is, but you
do know that the day does not change from year to
year.  You know that, for example, if he lies to you
on any January 1st, he will lie to you on every
January 1st, although you have already determined
that January 1st is not his lying day.

That is, you did not know his schedule until just
now, when he told you that he will lie 365 days from
now.  What day is it now, and what day will he lie?