
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:
\[g(A) = \frac{\sin A(4\cos^{2}A + 2\cos^{4}A + 2\sin^{2}A + \sin^{2}A \cos^{2}A)}{\tan A (\sec A - 2\sin A \tan A)}\]
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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