
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
\[g(x) = \frac{\sin^3 x + 5 \sin^2 x + 2\sin x + 3 \cos^2 x - 9}{\sin x + 1},\]
as $x$ ranges over all real numbers such that $\sin x \neq -1.$ Enter your answer using interval notation.

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