
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: 

$$\frac{\left(1+\frac{1}{2}\right)^{2} \times\left(1+\frac{1}{3}\right)^{2} \times\left(1+\frac{1}{4}\right)^{2} \times\left(1+\frac{1}{5}\right)^{2} \times \cdots \times\left(1+\frac{1}{10}\right)^{2}}{\left(1-\frac{1}{2^{2}}\right) \times\left(1-\frac{1}{3^{2}}\right) \times\left(1-\frac{1}{4^{2}}\right) \times\left(1-\frac{1}{5^{2}}\right) \times \cdots \times\left(1-\frac{1}{10^{2}}\right)}$$

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