
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 system of equations below? 
\[\begin{array}{l} x^2-4xy+3y^2-z^2=24 \\ -x^2+3yz+5z^2=60 \\ x^2+2xy+5z^2=85\\ \end{array}\]
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}
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