
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 three-digit integers that are not palindromes, like 352, a person can create a palindrome by repeatedly reversing the number, adding 3 to the reverse, and then adding the original number to this modified reverse. For example, $352 + (253+3) = 608$. Then, continue this process with $608 + (806+3) = 1417$ and so on. For all positive integers between 100 and 400, identify and sum the non-palindrome integers that take exactly five steps to become palindromes.

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