
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 the function $f(x) = \begin{cases} \sin x, & x \leqslant 0 \\ -\sin x, & x > 0 \end{cases}$, determine the correct conclusion among the following options:
A) $f(x)$ is an odd function
B) $f(x)$ is an even function
C) $f(x)$ is a periodic function
D) $f(x)$ is a decreasing function on $\left[-\frac{\pi}{2} + 2k\pi, \frac{\pi}{2} + 2k\pi\right]$ where $k \in \mathbb{Z}$

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