
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
Square  $S_1$  is inscribed inside circle  $C_1$ , which is inscribed inside square  $S_2$ , which is inscribed inside circle  $C_2$ , which is inscribed inside square  $S_3$ , which is inscribed inside circle  $C_3$ , which is inscribed inside square  $S_4$ .

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Let  $a$  be the side length of  $S_4$ , and let  $b$  be the side length of  $S_1$ . What is  $\tfrac{a}{b}$ ?

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