
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
Four special prizes at a school sports day are hidden beneath each chair numbered with two-digit positive integers. The first three numbers found are 45, 26, and 63, but the label on the last chair is partially ripped, leaving the number unreadable. The sum of the digits of all four numbers equals one-third of the sum of all four numbers. Additionally, the total sum of all numbers must be a multiple of 7. What is the smallest possible number for the fourth chair?

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