
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
Evaluate the expression $3 \cdot 2^{-(2k+2)} - 2^{-(2k+1)} + 2 \cdot 2^{-2k}$.
**A)** $\frac{9}{2} \cdot 2^{-2k}$  
**B)** $\frac{1}{2} \cdot 2^{-2k}$  
**C)** $\frac{9}{4} \cdot 2^{-2k}$  
**D)** $9 \cdot 2^{-2k}$  
**E)** $\frac{3}{4} \cdot 2^{-2k}$

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