
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
Define a function $f(x)$ on $\mathbb{R}$ that satisfies $f(-x) = -f(x)$, and $f\left(x + \frac{\pi}{2}\right) = f\left(x - \frac{\pi}{2}\right)$. Also, when $x \in \left[0, \frac{\pi}{2}\right]$, $f(x) = \sin x$. Determine the value of $f\left(\frac{5\pi}{3}\right)$.

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