
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
a) Derive Vieta's formula from the result of problem 137.

b) What is the value of the infinite product

$$
\begin{aligned}
& \frac{1}{2} \cdot \sqrt{\frac{1}{2}+\frac{1}{2} \cdot \frac{1}{2}} \cdot \sqrt{\frac{1}{2}+\frac{1}{2} \sqrt{\frac{1}{2}+\frac{1}{2} \cdot \frac{1}{2}}} \times \\
& \times \sqrt{\frac{1}{2}+\frac{1}{2} \sqrt{\frac{1}{2}+\frac{1}{2} \sqrt{\frac{1}{2}+\frac{1}{2} \cdot \frac{1}{2}}}} \ldots ?
\end{aligned}
$$

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