
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
Let's denote the amount paid by the fourth boy as $x$. The first boy paid $\frac{1}{2}\left(x + y + z\right)$, the second boy paid $\frac{1}{3}\left(x + y + z\right)$, and the third boy paid $\frac{1}{4}\left(x + y + z\right)$.

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