
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
A slip of paper fell out of a fortune cookie listing three two-digit numbers as 34, 18, and 73, which are visible but partially smeared, and obscures the fourth number completely. If the sum of the digits of all four numbers amounts to $\frac{1}{6}$ of the total sum of the four numbers, find the smallest fourth number such that its digits are in strictly increasing order.

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