
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 has a probability of $\frac{3}{4}$ of landing heads and $\frac{1}{4}$ of landing tails on each toss. The outcomes of the tosses are independent. The probability of winning Game C, where the player tosses the coin four times and wins if either all four outcomes are heads or all four are tails, can be compared to the probability of winning Game D, where the player tosses the coin five times and wins if the first two tosses are the same, the third toss is different from the first two, and the last two tosses are the same as the first two. Determine the difference in the probabilities of winning Game C and Game D.

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