
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
Translate the function $f(x)=1-2\sqrt{3}\cos^2{x}-(\sin{x}-\cos{x})^2$ by shifting its graph to the left by $\dfrac{\pi}{3}$ units to obtain the graph of the function $y=g(x)$. If $x\in\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$, then the interval of monotonic increase for the function $g(x)$ is ______.

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