
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 miser knight stores gold coins in 77 chests. One day, while recounting them, he noticed that if he opened any two chests, he could redistribute the coins so that they are evenly divided between the two chests. Then he noticed that if he opened any 3, or any 4, ..., or any 76 chests, he could also redistribute the coins so that an equal number of coins were in each of the opened chests. At this point, he heard a knock on the door and the old miser did not check whether he could redistribute the coins evenly among all 77 chests. Can a definitive answer be given to this question without looking inside the chests?

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