
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
Ruda received an alarm clock for his birthday. He was happy with it and set it to the exact time. Since then, every morning when he woke up (including Saturdays, Sundays, and holidays), he pressed the button that lights up the dial for exactly 4 seconds. During the time the button was pressed, the clock stopped. Otherwise, the clock neither gained nor lost time. On the afternoon of December 11, Ruda checked his clock and found that it was exactly 3 minutes behind the correct time.

When did Ruda receive this alarm clock?

Hint: How many times did Ruda press the button?

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