
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
Alice has a coin that lands heads with a probability of $\frac{1}{4}$, and Bob has a coin that lands heads with a probability of $\frac{3}{7}$. Alice and Bob alternately toss their coins until someone gets a head; the first one to get a head wins. Alice goes first. However, Alice can only win if she gets heads on an odd-numbered turn. Calculate the probability that Alice wins the game.
A) $\frac{1}{4}$
B) $\frac{3}{7}$
C) $\frac{7}{19}$
D) $\frac{9}{28}$
E) $\frac{1}{3}$

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