
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
Matthew writes a list of all three-digit squares backwards. For example, in his list, Matthew writes the three-digit square '625' as '526'. Norma notices that some numbers in Matthew's list are prime numbers. What is the mean of those prime numbers in Matthew's list?

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