
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 $f(x) = \cos{x} \cdot \sin{(x + \frac{\pi}{3})}-\sqrt{3}\cos^2{x} + \frac{\sqrt{3}}{4}$, where $x \in \mathbb{R}$.
(1) Find the minimum positive period and the monotonically increasing interval of the function $f(x)$;
(2) Find the range of the function $f(x)$ on the interval $[-\frac{\pi}{4}, \frac{\pi}{3}]$.

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