Task-oriented dialogue about: train

I'm looking for a train to broxbourne.
Where would you like to leave from, and what day and time would you like to travel?
I'm going to be leaving from Cambridge. I need to leave on Tuesday by 13:00.
Is there a time you would like to get there by ?
I don't have an arrival preference.
The earliest train leaves at 5:01. The latest train leaving by 13:00 would depart at 12:01. There is also one that leaves at 13:01. The trains run every hour.
Actually, I'd like to arrive by 13:00. Could you give me the train ID for the train arriving closest to that time?
Train ID is TR6357. Would you like to book ?