
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 passwords, $A$, $B$, $C$, and $D$. Each week, one of these passwords is used, and each week the password is chosen at random and equally likely from the three passwords that were not used in the previous week. If password $A$ is used in the first week, what is the probability that password $A$ will also be used in the seventh week? (Express your answer as a simplified fraction.)

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