
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
Calculate the product \(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\ldots\left(1-\frac{1}{11^2}\right)\left(1-\frac{1}{12^2}\right)\).
**A)** \(\frac{1}{12}\)  
**B)** \(\frac{13}{24}\)  
**C)** \(\frac{1}{24}\)  
**D)** \(\frac{13}{12}\)  
**E)** \(\frac{1}{6}\)

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