
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
Determine the range of the function
\[g(A) = \frac{\cos A(2\sin^{2}A + \sin^{4}A + 2\cos^{2}A + \cos^{2}A\sin^{2}A)}{\cot A (\csc A - \cos A\cot A)}\]
if \(A \neq n\pi\) for any integer \(n\).

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