Sort dates in mm/dd/yy and dd/mm/yy where I know the month they are from

I have a column of date strings I know are from a single month, in this case the dates are all between January and February 2020. I want to sort them in ascending order. However, they are in different formats some in mm/dd/yy, some in dd/mm/yy. How can I sort them?

data = {
    'date': ['1/1/2020','20/1/2020', '1/1/2020', '1/28/2020','21/1/2020', '1/25/2020', '29/1/2020'],
}


df = pd.DataFrame(data)

print(df)

Edit

Another sample of dates I'd like to be sorted

import pandas as pd

data = {'Tgl': {
  1: '1/1/2023',
  2: '1/1/2023',
  3: '1/3/2023',
  4: '1/5/2023',
  5: '1/5/2023',
  6: '1/9/2023',
  7: '10/1/2023',
  8: '12/1/2023',
  9: '16/1/2023'}}

df = pd.DataFrame(data)

df = pd.to_datetime(df['Tgl'])

df = pd.to_datetime(df['Tgl'], dayfirst = True)

In the provided example, there is limited ambiguity as you don't have cases for which a day ≤ 12 is different from the month.

So you can use pandas.to_datetime(pd.to_datetime(df['date'])) to convert to a clean datetime, or, to sort while keeping the original strings:

df.sort_values(by='date', key=pd.to_datetime)

Output:

       date
0   1/1/2020
2   1/1/2020
1  20/1/2020
4  21/1/2020
5  1/25/2020
3  1/28/2020
6  29/1/2020

If you have ambiguous dates (like 1/2/2020) you can choose to give priority to days/months with the dayfirst parameter:

df.sort_values(by='date', key=lambda x: pd.to_datetime(x, dayfirst=True))

Example:

        date
2   2/1/2020  # Jan 2nd
1  20/1/2020
4  21/1/2020
5  1/25/2020
3  1/28/2020
6  29/1/2020
0   1/2/2020  # Feb 1st

custom logic

Let's assume the first number is the day, unless the value is > 2, in which case we convert it to month.

def custom_date(s):
    return (
      pd.to_datetime(s, dayfirst=True)
        .mask(lambda x: x.dt.month>2,
              pd.to_datetime(s, dayfirst=False))
    )

df.sort_values(by='date', key=custom_date)

Output (with an additional column to see the result of the custom conversion):

        date  converted
2   2/1/2020 2020-01-02
7  10/1/2020 2020-01-10 # both converted 
8  1/10/2020 2020-01-10 # to Jan 10
1  20/1/2020 2020-01-20
4  21/1/2020 2020-01-21
5  1/25/2020 2020-01-25
3  1/28/2020 2020-01-28
6  29/1/2020 2020-01-29
0   1/2/2020 2020-02-01