
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
Given the function $f(x) = \sqrt{3}\sin x \cos x + \cos^2 x - \frac{1}{2}$, the graph of $y = g(x)$ is obtained by shifting the graph of $f(x)$ to the left by $\frac{5\pi}{12}$ units. Find the range of $g(x)$ on the interval $\left[-\frac{\pi}{12}, \frac{\pi}{3}\right]$.

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