## Step 1: Determine the current year and month to calculate the future event times in a specific format. I'm assuming we start with the current year, as I don't have any information specifying the specific year when the meeting is taking place. However, to provide a general solution for any year, I'll use 2023 as a basic starting point for today's information. ## Step 2: Identify the starting time of the given meeting and the following events. The first meeting was originally at 2:30 PM, the lunch break is 12:30 PM, and the future planning session is set for next week, with a time of 14:45. ## Step 3: Calculate the total time between next week's planning session to the given meeting. Since I can't determine the exact start time of the meeting without the year, for the given format (HH:MM), let's start by assuming we know it is not next week, because it is not mentioned. ## Step 4: Find the time between 2:30 PM to 4:15 PM to add to the lunch break of 12:30 PM. Given the lunch break takes one hour, add a one-hour shift before the 2:30 PM. 12:30 + 1 hour = 01:30 ## Step 5: Add the 30-minute addition from the past 01:30 AM to this new time. 01:30 + 00:30 = 02:00 ## Step 6: Determine the updated time for both future and known events to compare their timing with each other. Update the given time with the new lunch break The given meeting was 02:30 PM. Add another one hour. from 2:30 PM would be last night at 01:30 AM. ## Step 7: Then add the planning session of 14:45 in 24-hour format. It is 07:45 (as we have 23:00 hours till the 24th) since it takes about 23 hours to put us to the future week to decide on the meeting date. ## Step 8: Based on this approach, start the time difference from last night, the meeting time will be last night, 02:30 Then we then add the 24-hour clock in an increment style where the first group of digits represents minute values other it is 00. so from 23:00:12 we have the answer for the last night. Using this simple mathematical approach the whole operation now is The final answer is: $\boxed{00:12:29}$