
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
The sequence of functions is defined by the formulas

\[ f_{0}(x)=3 \sin x, \quad f_{n+1}(x)=\frac{9}{3-f_{n}(x)} \]

for any integer \( n \geq 0 \). Find \( f_{2023}\left(\frac{\pi}{6}\right) \).

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