
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 $\frac{2}{3}$ and tails with $\frac{1}{3}$. A player can choose between Game C and Game D. In Game C, the player tosses the coin five times and wins if either the first three or the last three outcomes are all the same. In Game D, she tosses the coin five times and wins if at least one of the following conditions is met: the first two tosses are the same and the last two tosses are the same, or the middle three tosses are all the same.
A) Game C has a higher probability of $\frac{5}{81}$ over Game D.
B) Game D has a higher probability of $\frac{5}{81}$ over Game C.
C) Game C has a higher probability of $\frac{29}{81}$ over Game D.
D) Game D has a higher probability of $\frac{29}{81}$ over Game C.

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