
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 value of the product 
\[
\prod_{k=1}^{50} \left(\frac{\sqrt{(2k-1)(2k+1)}}{(2k)^2}\right)
\]
**A)** 0.071
**B)** 0.171
**C)** 0.271
**D)** 0.371
**E)** 0.471

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