
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 simplified expression and range of the function
\[f(x) = \frac{\sin^3 x + 5 \sin^2 x + 2\sin x - 3\cos^2 x - 9}{\sin x - 2}\]
as $x$ ranges over all real numbers such that $\sin x \neq 2.$ (Note: The restriction is trivially true since $\sin x$ can never equal 2.)

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