
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
Let $f(x)$ be a function defined on $\mathbb{R}$ with the smallest positive period of $\frac{5\pi}{3}$, and on $[-\frac{2\pi}{3}, \pi)$, let $f(x)$ be defined as follows:
$$
f(x) = \begin{cases}
\sin{x} & , x \in [-\frac{2\pi}{3}, 0) \\
\cos{x} & , x \in [0, \pi)
\end{cases}
$$
Find the value of $f\left(-\frac{16\pi}{3}\right)$.

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