
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 certain intelligence station has four different kinds of passwords $A$, $B$, $C$, and $D$. Each week, one of these passwords is used, and each week a password is chosen uniformly at random from the three passwords that were not used the previous week. Given that password $A$ is used in the first week, what is the probability that password $A$ is also used in the seventh week? (Express your answer in the simplest fractional form.)

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