
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
Given the system of equations:
\begin{align*}
xy + 3x + 4y + 10 &= 30,\\
yz + 4y + 2z + 8 &= 6,\\
xz + 4x + 3z + 12 &= 30,
\end{align*}
find the positive solution for $x$.

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