
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
\[ g(A) = \frac{\sin A(5\cos^{2}A + 2\cos^{4}A + 2\sin^{2}A + \sin^{2}A\cos^{2}A)}{\tan A (\csc A - \sin A\tan A)} \]
if \( A \neq \dfrac{n\pi}{2} \) for any integer \( n \). Use interval notation for your answer.

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