
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A kitchen clock loses 2 seconds per day, and an antique clock in the room gains 15 seconds per day. On Sunday at noon, the kitchen clock shows 12:01, and the antique clock shows 11:59. During the week, when will the sum of the squares of the differences between the clocks' displayed times and the actual time be minimized?

Present the answer in LaTex format: \boxed{Your answer}
user