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

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