Sql-server – Correcting and Detecting overlapped dates with CTE

I have a CTE that marks (as bits) overlapped records based on certain criteria. After filtering, I need to update these records to "correct" them and make them sequential, but I'm getting a 4104 on the update statement because I'm calling variables that are stored outside the CTE's queries.

When I directly call the bit variable I don't have problems, but where I do a calculation with t2.ini (which is one of variables in the subquery) I get the error. I've been stuck for days and I can't find a better approach for a better solution.

In this table, for this user we have two overlapped records with id 2 and 3

valido id          idhr       ini                     fin                      ult_act
------ ----------- ---------- ----------------------- ----------------------- -----------------------
1      1           666        2019-12-01 00:00:00.000 2019-12-05 00:00:00.000 2018-01-10 00:00:00.000
1      2           666        2019-12-03 00:00:00.000 2019-12-07 00:00:00.000 2018-01-12 00:00:00.000
1      3           666        2019-12-06 00:00:00.000 2019-12-10 00:00:00.000 2018-01-14 00:00:00.000
1      4           666        2019-12-15 00:00:00.000 2019-12-20 00:00:00.000 2018-01-16 00:00:00.000

With my current code I'm able to set overlapped records as 0 and keep the latest added (ult_act is a timestamp for when this record was added) as 1.

valido id          idhr          ini                   fin                     ult_act
------ ----------- ---------- ----------------------- ----------------------- -----------------------
1      1           666        2019-12-01 00:00:00.000 2019-12-05 00:00:00.000 2018-01-10 00:00:00.000
0      2           666        2019-12-03 00:00:00.000 2019-12-07 00:00:00.000 2018-01-12 00:00:00.000
1      3           666        2019-12-06 00:00:00.000 2019-12-10 00:00:00.000 2018-01-14 00:00:00.000
1      4           666        2019-12-15 00:00:00.000 2019-12-20 00:00:00.000 2018-01-16 00:00:00.000

But I need to also make the dates sequential so in the table it would look like INI→FIN→INI→FIN →… without overlapped dates. To accomplish that I thought of grabbing the overlapped row and the INI value, substract one (day) and overwrite it on the FIN value of the last record or something like this:

FIN = (T2.INI - 1) --LAST ENDDATE RECORD = (OVERLAPPED BEGININGDATE RECORD -1)

This is the current code that gives me an error. I received a suggested to do an UPDATE with JOIN, but with IDOR column that's temporarily generated it isn't possible to work it around:

CREATE TABLE tstOver 
    ([valido] int, [id] int, [idhr] int, [ini] datetime, fin datetime, ult_act datetime)
;

INSERT INTO tstOver
VALUES
    (1, 1, 666, '2019-12-01','2019-12-05','2018-01-10'),
    (1, 2, 666, '2019-12-03','2019-12-07','2018-01-12'),
    (1, 3, 666, '2019-12-06','2019-12-10','2018-01-14'),
    (1, 4, 666, '2019-12-15','2019-12-20','2018-01-16')
;

;WITH CTE AS
(
    --GROUP BY IDHR
    SELECT ROW_NUMBER() OVER (PARTITION BY IDHR ORDER BY ULT_ACT ASC) AS IDOR,
    T.VALIDO,
    T.ID,
    CONVERT(VARCHAR,T.INI,112) AS INI,
    CONVERT(VARCHAR,T.FIN,112) AS FIN,
    CONVERT(VARCHAR,T.ULT_ACT,112) AS ULT_ACT
    FROM tstOver T
        WHERE EXISTS
            (
                --CRITERIA FOR OVERLAPS
                SELECT 1 FROM tstOver T2
                WHERE T.ID <> T2.ID AND
                    (T2.INI BETWEEN T.INI AND T.FIN) OR
                    T2.INI = T.FIN
            )
)
    --SETTING VALIDO TO 0 WHEN THEY OVERLAP AND MAKING RECORDS SEQUENTIAL DATE-WISE
    UPDATE CTE SET VALIDO = 0, FIN = (T2.INI - 1) --4406 BECAUSE T2.INI IT'S DERIVED FROM THE SUBQUERY
    WHERE IDOR > 1

    SELECT * FROM TSTOVER
GO


DROP TABLE tstOver

Any help is appreciated.