
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
The passenger ship "Happy" arrives in a seaport once every 3 days, the ship "Lucky" once every 4 days, and the ship "Hopeful" once every 5 days. All three ships were in port last Monday. After how many days will all three ships arrive at the port together again and what day of the week will it be?

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