SQL How to determine the duration of the action based on the current and next event?

I have a table with two columns: the action start time and the name of action.

I need to know the duration of the action: start and end time. The start time is the time of the action, which is already known.
But how to know the end time? That is, the beginning of the next action different from the current one?

Example for the action "walking"

Please see the corrected version underneath. This one assumes that each action is unique.
> I think you could use the lag function to achieve your goal.
>
> select
> action,
> time as time_start,
> lag(time, -1) over(order by time) as time_end
> from <table_name>
>
> In this case the time_end for the last row will be equal to NULL,
> which I think is correct, as it isn't known yet.

EDIT: After the remark from @Tim Biegeleisen, this is the updated answer, built upon his work. However, it correctly finds the time_end value for groups of the same, consecutive actions.

WITH data AS (
    SELECT '2023-07-27 04:52:00.000' AS time, 'running' AS action UNION ALL
    SELECT '2023-07-27 04:53:00.000', 'running' UNION ALL
    SELECT '2023-07-27 04:55:00.000', 'walking' UNION ALL
    SELECT '2023-07-27 04:59:00.000', 'walking' UNION ALL
    SELECT '2023-07-27 05:01:00.000', 'sitting' UNION ALL
    SELECT '2023-07-27 05:06:00.000', 'walking' UNION ALL
    SELECT '2023-07-27 05:10:00.000', 'walking' UNION ALL
    SELECT '2023-07-27 05:12:00.000', 'walking' UNION ALL
    SELECT '2023-07-27 05:15:00.000', 'walking' UNION ALL
    SELECT '2023-07-27 05:20:00.000', 'running' 
),
withLag AS (
    SELECT 
        action,
        time AS start_time,
        LAG(time) OVER (ORDER BY time desc) AS next_time,
        ROW_NUMBER() OVER (ORDER BY time) AS row_num,
        ROW_NUMBER() OVER (PARTITION BY action ORDER BY time) AS group_num
    FROM data
)
SELECT action, min(start_time) as time_start, max(next_time) as time_end
FROM withLag
GROUP BY action, row_num - group_num
order by time_start

As a result we achieve the expected outcome:

Using the difference in row numbers method we can try the following:

<!-- language: sql -->

WITH cte AS (
    SELECT *, ROW_NUMBER() OVER (ORDER BY time) rn1,
              ROW_NUMBER() OVER (PARTITION BY action ORDER BY time) rn2
    FROM yourTable
)

SELECT MIN(time) AS time_start,
       MAX(time) AS time_end,
       action
FROM cte
GROUP BY rn1 - rn2, action
ORDER BY MIN(time);

<h2>Demo</h2>