
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
If the digits of a natural number can be divided into two groups such that the sum of the digits in each group is equal, the number is called a "balanced number". For example, 25254 is a "balanced number" because $5+2+2=4+5$. If two adjacent natural numbers are both "balanced numbers", they are called a pair of "twin balanced numbers". What is the sum of the smallest pair of "twin balanced numbers"?

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