
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
Determine the value of \( y \) that satisfies the equation \( 10^y \cdot 1000^{y} = 100^{8y-4} \).
**A)** \( \frac{1}{2} \)   
**B)** \( \frac{3}{4} \)   
**C)** \( \frac{2}{3} \)    
**D)** \( 1 \)    
**E)** \( \frac{5}{3} \)

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