
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
An unfair coin comes up heads with probability \(\frac{4}{7}\) and tails with probability \(\frac{3}{7}\). Aerith and Bob take turns flipping the coin until one of them flips tails, with Aerith going first. What is the probability that Aerith wins the game?

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