
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 flips a coin, with the probability of landing heads being $\frac{1}{3}$. Brian also flips a coin, with the probability of landing heads being $\frac{2}{5}$. Amelia and Brian take turns flipping their coins, and the first one to get heads wins. Amelia starts. Calculate the probability that Amelia wins expressed as $\frac{p}{q}$, where $p$ and $q$ are coprime positive integers.

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