
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
Let \( f_{1} = 9 \) and 
\[ f_{n} = \begin{cases} 
f_{n-1} + 3 & \text{if } n \text{ is a multiple of } 3 \\
f_{n-1} - 1 & \text{if } n \text{ is not a multiple of } 3 
\end{cases} \]
If \( B \) is the number of possible values of \( k \) such that \( f_{k} < 11 \), determine the value of \( B \).

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