
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
\[ g(x) = \frac{\sin^3 x + 4 \sin^2 x + 2 \sin x + 3 \cos^2 x - 9}{\sin x - 2}, \]
as \( x \) ranges over all real numbers such that \( \sin x \neq 2 \) (note this condition is inherently satisfied since \( \sin x \) is always between -1 and 1).

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