
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 $f(x)=\sin^2{x} - \cos^2{x} - 2\sqrt{3}\sin{x}\cos{x}$ for $x \in \mathbb{R}$.
(Ⅰ) Find the value of $f\left(\frac{2\pi}{3}\right)$.
(Ⅱ) Determine the smallest positive period of $f(x)$ and the intervals where $f(x)$ is monotonically increasing.

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