
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
Suppose $x, y, z$ are integers from the set of positive integers less than $9$ such that:
\begin{align*}
xyz &\equiv 1 \pmod{9}, \\
7z &\equiv 4 \pmod{9}, \\
8y &\equiv 5 + y \pmod{9},
\end{align*}
find the remainder when $x+y+z$ is divided by $9$.

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