
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
\[ g(x) = \frac{\cos x (2\sin^2 x + \sin^4 x + 2\cos^2 x + \cos^2 x \sin^2 x)}{\cot x (\csc x - \cos x \cot x)} \]
for \( x \neq n\pi \) where \( n \) is any integer.

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