
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 the ancient Chinese mathematical work "Zhang Qiu Jian Suan Jing," there is a problem known as the Hundred Chickens Problem: "There are cocks that cost five coins each, hens that cost three coins each, and chicks, three of which cost one coin. With a total of one hundred coins, one wants to buy one hundred chickens. How many cocks, hens, and chicks can one buy?" Let the number of cocks, hens, and chicks be $x$, $y$, and $z$ respectively. Then, we have the system of equations: 
$$
\begin{cases} 
x+y+z=100 \\ 
5x+3y+\frac{1}{3}z=100
\end{cases}
$$
When $z=81$, find the values of $x$ and $y$.

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