
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
If $x, y, z$ are non-negative integers less than $9$ such that:
\begin{align*}
x + 3y + 2z &\equiv 0 \pmod{9}, \\
3x + 2y + z &\equiv 5 \pmod{9}, \\
2x + y + 3z &\equiv 5 \pmod{9},
\end{align*}
then determine the remainder when $xyz$ is divided by $9$.

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