[Python] Sort a list of lists when one of the sort items is text month

I am trying to sort this list of lists by the year and then by month,I can get the years part sorted but am stuck when I try to do secondary sort by month. I have created a dict and a list to try to use to sort.

my code:

from operator import itemgetter

import pandas as pd

month_list = ["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
months = {
'Jan': 0,
'Feb': 1,
'Mar': 2,
'Apr': 3,
'May': 4,
'Jun': 5,
'Jul': 6,
'Aug': 7,
'Sep': 8,
'Oct': 9,
'Nov': 10,
'Dec': 11,
}
data = [['Sep', '2024', 112], ['Dec', '2022', 79], ['Apr', '2023', 114], ['Aug', '2024', 194], ['May', '2022', 140], ['Jan', '2023', 222]]

half_sorted = sorted(data, key=itemgetter(1))
input(half_sorted)


My Output so far:

[['Dec', '2022', 79], ['May', '2022', 140], ['Apr', '2023', 114], ['Jan', '2023', 222], ['Sep', '2024', 112], ['Aug', '2024', 194]]

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