
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:
\[ g(A) = \frac{\cos A (5\sin^2 A + \sin^4 A + 5\cos^2 A + \cos^3 A\sin A)}{\cot A (\csc A - \cos A\cot A)} \]
for \( A \neq \frac{n\pi}{2} \) where \( n \) is any integer.

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