
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 probability $\frac{1}{4}$, and Blaine has a coin that lands on heads with probability $\frac{3}{7}$. They toss their coins alternately starting with Amelia until one of them gets a head, at which point the person who tossed the head wins. Calculate the probability Amelia wins the game.
A) $\frac{1}{2}$
B) $\frac{5}{16}$
C) $\frac{7}{16}$
D) $\frac{9}{16}$
E) $\frac{11}{16}$

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