
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
An isosceles triangle with a base of length $b$ and equal sides each of length $s$ is used to form a new isosceles triangle by joining the midpoints of its sides. This process is repeated indefinitely. Calculate both the limit of the sum of the perimeters and the limit of the sum of the areas of all triangles thus formed.

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