
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
Solve the following system of equations: 
\[
\begin{align*}
4x - 6y + 2z &= -14, \\
8x + 3y - z &= -15, \\
3x + z &= 7.
\end{align*}
\]
Express your answer as an ordered triple \((x, y, z)\).

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