What is meant by ''set' object is not subscriptable' and how do i remove it from my code

Question: implement a program that prompts the user for a date, anno Domini, in month-day-year order, formatted like 9/8/1636 or September 8, 1636. Then output that same date in YYYY-MM-DD format. If the user’s input is not a valid date in either format, prompt the user again. Assume that every month has no more than 31 days; no need to validate whether a month has 28, 29, 30, or 31 days.

My Solution: Comments are before each part in the code. On line 44, (marked in aesteriks (*)) it shows "TYPEERROR: 'set' is not subscriptable when i input the date : January 12, 1234. I dont know what it means or what I'm doing wrong. What that part is supposed to do is store the month's number from the list and update the variable month.

Here's my code:

#define list
months = { "January", "1"
"February", "2"
"March","3"
"April","4"
"May","5"
"June","6"
"July","7"
"August","8"
"September","9"
"October","10"
"November","11"
"December""12"
}
#input date
date_input = input("Date: ")
#loop
while True:
try:
#MONTH---------------------------------------------------------------------------
if "/" in date_input:
month, day, year = date_input.split("/")
month = month
break
elif " " in date_input and "," in date_input:
month, day, year = date_input.split(" ")
day = day.replace(",", "")
break
else:
date_input = input("Date: ")
except ValueError:
pass
while True:
try:
#MONTH------------------------------------------------------------------------------
if month.isalpha():
for item in months:
if month == item:
**month = (f"{int(months[item]):02}")**
break
elif month.isdigit():
month = int(month)
if month > 0 and month < 13:
if month > 0 and month < 10:
month = (f"{int(month):02}")
break
else:
date_input = input("Date: ")
break
except ValueError:
pass
while True:
try:
#DAY---------------------------------------------------------------------------
if int(day) > 0 and int(day) < 32:
if int(day) > 0 and int(day) < 10:
day = (f"{int(day):02}")
day = int(day)
break
except ValueError:
pass
print(year, "-", month, "-", day, sep="")

months = { "January", "1"
"February", "2"
"March","3"
"April","4"
"May","5"
"June","6"
"July","7"
"August","8"
"September","9"
"October","10"
"November","11"
"December""12"
}

is a set, not dict. May be you want

months = { "January": "1",
"February": "2",
"March": "3",
"April": "4",
"May": "5",
"June": "6",
"July": "7",
"August": "8",
"September": "9",
"October": "10",
"November": "11",
"December":"12"
}