
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
Given a geometric progression with the first term $a$, common ratio $r$ (where $-1 < r < 1$), and a constant $c$, find the sum of the series formed by multiplying each term squared by $c$, where the series is $ca^2, ca^2r^2, ca^2r^4, \ldots$.

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