
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 game is played with four integers in the following manner: add three of these numbers, divide that sum by 3, and add the result to the fourth number. There are four ways to play this game, yielding the following results: 17, 21, 23, and 29. What is the largest of the four numbers?

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