
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 an even function defined on $\mathbb{R}$ such that $f(x + \pi) = f(x)$, and $f(x) = \sin x$ when $x \in \left[0, \frac{\pi}{2}\right]$. Find the value of $f\left(\frac{5\pi}{3}\right)$.

A) $- \frac{1}{2}$
B) $\frac{\sqrt{3}}{2}$
C) $- \frac{\sqrt{3}}{2}$
D) $\frac{1}{2}$

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