
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
Given $f(x)$ be a function with domain $\mathbb{R}$ and the smallest positive period of $2\pi$, and given by 
$$
f(x) =
\begin{cases}
\sin x & \text{for } 0 \le x \le \pi, \\
\cos x & \text{for } -\pi < x < 0,
\end{cases}
$$
find the value of $f\left(-\frac{13\pi}{4}\right)$.

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