
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
Consider a geometric progression where the first term is $b$ and the common ratio is $s$, with $|s| < 1$. If every term from the third term onwards is multiplied by a constant $c$ before squaring, calculate the sum of the squares of the resulting modified sequence.
A) $\frac{c^2b^2s^3}{1 - s}$
B) $\frac{cb^2s^4}{1 - s^2}$
C) $\frac{c^2b^2s^4}{1 - s}$
D) $\frac{c^2b^2}{1 - s^4}$
E) None of these

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