
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
Suppose a function $f(x)$, where $x \in \mathbb{R}$, satisfies $f(x + \pi) = f(x) + \sin x$. When $0 \leq x < \pi$, $f(x) = 0$. Then, find the value of $f\left( \frac{23\pi}{6} \right)$.

A) $\frac{1}{2}$

B) $\frac{\sqrt{3}}{2}$

C) 0

D) $-\frac{1}{2}$

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