
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
Calvin joins Amelia and Blaine in their coin-tossing game. Amelia's coin now lands heads with probability $\frac{1}{4}$, Blaine's coin with probability $\frac{1}{3}$, and Calvin's with probability $\frac{1}{2}$. The three players toss their coins in the order Amelia, Blaine, Calvin, and repeat this order until one of them gets a head, winning the game. Amelia starts the game. Calculate the probability that Amelia wins the game.
A) $\frac{1}{4}$
B) $\frac{1}{3}$
C) $\frac{1}{2}$
D) $\frac{2}{3}$

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