
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 heads with probability $\frac{3}{7}$. Blaine goes first, and they alternatively toss their coins until someone gets a head or a maximum of five rounds are completed. The first one to get a head wins. If neither gets a head after five rounds, the game is a draw. Calculate the probability that Amelia wins.

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