
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
Find the range of the function
\[ g(x) = \left( \arccos \frac{x}{3} \right)^2 + 2\pi \arcsin \frac{x}{3} - 3\left( \arcsin \frac{x}{3} \right)^2 + \frac{\pi^2}{4} (x^2 - 3x + 9). \]

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