
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
In a virtual puzzle game, three two-digit positive integers are shown as part of the code to unlock a level: 34, 56, and 45. However, the final part of the code is blurred, only showing it as a two-digit number. If the sum of the digits of all four numbers is $\frac{1}{3}$ of their total sum, what could be the smallest fourth number in the sequence?

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