
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
Three people \(A\), \(B\), and \(C\) play a game of passing a basketball from one to another. Find the number of ways of passing the ball starting with \(A\) and reaching \(A\) again on the 11th pass. For example, one possible sequence of passing is:
\[ A \rightarrow B \rightarrow A \rightarrow B \rightarrow C \rightarrow A \rightarrow B \rightarrow C \rightarrow B \rightarrow C \rightarrow B \rightarrow A . \]

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