
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
Let 
\[ g(x) = (\arctan x)^2 - \arctan x \cdot \arccot x + (\arccot x)^2. \] 
Find the range of $g(x)$ for all $x$ in the real numbers excluding the singular points where the functions are not defined.

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