
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 the function $f(x)$ ($x \in \mathbb{R}$) satisfy $f(x+\pi)=f(x)+\sin x$. When $0 \leqslant x < \pi$, $f(x)=0$. Then, find the value of $f\left(\dfrac{23\pi}{6}\right)$.

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