SQL query to show user session length - sql

Question

I have a table that looks like this:
user_id page happened_at
2 'page3' 2017-10-05 11:31
1 'page2' 2016-02-01 00:02
2 'page1' 2017-10-05 15:24
3 'page3' 2017-03-31 19:35
4 'page1' 2017-07-09 00:24
2 'page3' 2017-10-05 15:28
1 'page3' 2018-02-01 13:02
2 'page2' 2017-10-05 16:14
2 'page3' 2017-10-05 16:34
etc
I have a query that identifies user sessions, which are opened pages #1, #2 and #3, in that particular order, made in a time period less than one hour from each other (page3 within an hour of page2, page2 within an hour of page1). Any pages, opened between that, can be ignored. Example of a session from the table above:
user_id page happened_at
2 'page1' 2017-10-05 15:24
2 'page2' 2017-10-05 16:14
2 'page3' 2017-10-05 16:34
My query so far looks like this and shows user_id of users, who had sessions:
select user_id
from (select user_id,page,happened_at,
lag(page) over(partition by user_id order by happened_at) as prev_page,
lead(page) over(partition by user_id order by happened_at) as next_page,
datediff(minute,lag(happened_at) over(partition by user_id order by happened_at),happened_at) as time_diff_with_prev_action,
datediff(minute,happened_at,lead(happened_at) over(partition by user_id order by happened_at)) as time_diff_with_next_action
from tbl
) t
where page='page2' and prev_page='page1' and next_page='page3'
and time_diff_with_prev_action <= 60 and time_diff_with_next_action <= 60
What I need is to edit a query, add 2 columns to the output, session start time and session end time, which is last action + 1 hour. Please advice how to make it. Temporary tables are forbidden, so it should be just a query. Example output should be:
user_id session_start session_end
2 2017-10-05 15:24 2017-10-05 17:34
Thanks for your time!