
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
On November 1, 2019, at exactly noon, two students, Gavrila and Glafira, set their watches (both have standard watches where the hands make a full rotation in 12 hours) accurately. It is known that Glafira's watch gains 12 seconds per day, and Gavrila's watch loses 18 seconds per day. After how many days will their watches simultaneously show the correct time again? Give the answer as a whole number, rounding if necessary.

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