
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
By successively calculating the lengths of chords $\left[D A||, D A_{1} \mid\right.$, $\left[D A_{2}\right] \ldots$, derive Euler's formula that gives the length of the arc $D A$:

$$
\breve{D A}_{\infty}=r \varphi=\lim _{n \rightarrow \infty} \frac{r \sin \varphi}{\cos \frac{\varphi}{2} \cdot \cos \frac{\varphi}{4} \cdot \cos \frac{\varphi}{8} \ldots \cos \frac{\varphi}{2^{n}}}
$$

Substitute here $\varphi=\frac{\pi}{2}$ and $r=1$, and write down the formula for calculating $\pi$ found by Viète.

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