
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
Define a sequence of real numbers \( b_1, b_2, b_3, \dots \) by \( b_1 = 2 \) and \( b_{n + 1}^2 = 50b_n^2 \) for all \( n \geq 1 \). Then \( b_{50} \) equals
**A)** \( 2 \cdot 50^{25} \)  
**B)** \( 2 \cdot 50^{24.5} \)  
**C)** \( 50^{49} \)  
**D)** \( 100^{24.5} \)  
**E)** None of these

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