
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
How many ordered triples \((x, y, z)\) of integers satisfy the following system of equations? 
\[
\begin{align*}
x^2 - 3xy + 2y^2 - z^2 &= 39, \\
-x^2 + 6yz + 2z^2 &= 40, \\
x^2 + xy + 8z^2 &= 96.
\end{align*}
\]
A) 0
B) 1
C) 2
D) A finite number greater than 2
E) Infinitely many

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