
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
Let \( x, y, \) and \( z \) be numbers such that:
\[2003z - 4006x = 1002\]
\[2003y + 6009x = 4004\]
Determine the average of \( x, y, \) and \( z \).
A\) \(\frac{1}{2}\) \\
B\) \(\frac{3}{4}\) \\
C\) \(\frac{5}{6}\) \\
D\) \(1\) \\
E\) \({\text{Not uniquely determined}}\)

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