
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
For some integers that are not palindromes, like 195, a person can create a palindrome by repeatedly reversing the number and adding the original number to its reverse. However, some integers, like 196, are believed not to result in a palindrome no matter how many times this operation is repeated. For the three-digit numbers, identify all numbers which become palindromes in exactly seven steps and calculate their sum.

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