
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 $\frac{1}{3}$. They alternately toss their coins, starting with Amelia, until someone gets a head or they both toss their coins 5 times without a head, resulting in a tie. All coin tosses are independent. Determine the probability that Amelia wins.
A) $\frac{1}{4}$
B) $\frac{15}{32}$
C) $\frac{1}{2}$
D) $\frac{1}{3}$

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