
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 court mathematician received his annual salary in silver thalers, which he arranged into nine piles that formed a magic square. The king admired this but regretted that none of the piles contained a prime number of coins.

- "If I had nine more coins," said the mathematician, "then by adding one coin to each pile, I would have a magic square consisting entirely of prime numbers."

The king confirmed this statement and was about to give the mathematician nine more thalers when the royal jester exclaimed, "Wait!" The jester removed one coin from each pile, and everyone saw that this also formed a new magic square, consisting entirely of prime numbers. Thus, the jester saved the king nine thalers.

What is the annual salary of the court mathematician?

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