
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
For $-1 < r < 1$, let $S(r)$ denote the sum of the geometric series \[18+18r+18r^2+18r^3+\cdots.\] Let $a$ between $-1$ and $1$ satisfy $S(a)S(-a) = 3024$. Find $S(a) + S(-a)$.

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