
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
A biased coin lands heads with a probability of $\frac{3}{4}$ and tails with a probability of $\frac{1}{4}$. Each toss is independent. For Game A, calculate the probability that the player wins by tossing the coin three times and obtaining all the same outcome, and for Game C, calculate the probability that the player wins by tossing the coin four times and obtaining all the same outcome.

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