
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
Tom and Geri have a competition. Initially, each player has one attempt at hitting a target. If one player hits the target and the other does not then the successful player wins. If both players hit the target, or if both players miss the target, then each has another attempt, with the same rules applying. If the probability of Tom hitting the target is always \(\frac{4}{5}\) and the probability of Geri hitting the target is always \(\frac{2}{3}\), what is the probability that Tom wins the competition?
A \(\frac{4}{15}\)
B \(\frac{8}{15}\)
C \(\frac{2}{3}\)
D \(\frac{4}{5}\)
E \(\frac{13}{15}\)

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