
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, exactly at noon, two students, Gavrila and Glafira, synchronized their watches perfectly (both students have standard watches with hands that complete a full revolution in 12 hours). It is known that Glafira's watch gains 36 seconds per day, while Gavrila's watch loses 18 seconds per day. After how many days will their watches simultaneously display the correct time again? Provide the answer as a whole number, rounding if necessary.

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