
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
Find the interval(s) where the function $y = \log_{\frac{1}{2}} \sin \left(2x + \frac{\pi}{4} \right)$ is decreasing.

A) $(k\pi - \frac{\pi}{4}, k\pi]$, where $k \in \mathbb{Z}$
B) $(k\pi - \frac{\pi}{8}, k\pi + \frac{\pi}{8}]$, where $k \in \mathbb{Z}$
C) $(k\pi - \frac{3\pi}{8}, k\pi + \frac{\pi}{8}]$, where $k \in \mathbb{Z}$
D) $(k\pi + \frac{\pi}{8}, k\pi + \frac{3\pi}{8}]$, where $k \in \mathbb{Z}$

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