
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
In base $R_1$, the repeating decimals for fractions $F_1$ and $F_2$ are $0.454545\ldots$ and $0.545454\ldots$, respectively. In base $R_2$, the fraction $F_1$ is represented as $0.383838\ldots$ and $F_2$ as $0.616161\ldots$. Determine the sum of $R_1$ and $R_2$, each written in base ten.
A) 24
B) 22
C) 21
D) 20
E) 19

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