
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
Amelia has a coin that lands heads with a probability of $\frac{3}{7}$, and Blaine has a coin that lands on heads with a probability of $\frac{1}{4}$. Initially, they simultaneously toss their coins once. If both get heads, they stop; otherwise, if either gets a head and the other a tail, that person wins. If both get tails, they start tossing their coins alternately as in the original scenario until one gets a head and wins. Amelia goes first in the alternate rounds. What is the probability that Amelia wins the game?
A) $\frac{5}{14}$
B) $\frac{9}{14}$
C) $\frac{11}{14}$
D) $\frac{13}{14}$
E) $\frac{1}{2}$

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