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

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