
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
If there exist two different points on the graph of the function $y=f(x)$ such that the tangents to the function's graph at these two points are perpendicular to each other, then the function $y=f(x)$ is said to have property $T$. If the function $g(x)=ax-\frac{c}{2}+bsinxcosx+c{cos^2}x$ has property $T$, where $a$, $b$, and $c$ are real numbers and satisfy $b^{2}+c^{2}=1$, then the range of the real number $a+b+c$ is ______.

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