
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 $f(x) = \sin(\frac{\pi}{6} - 2x) + \frac{3}{2}$, where $x \in \mathbb{R}$

1. Find the maximum value of the function $f(x)$ and the set of values of the independent variable $x$ when the maximum value is obtained.
2. Find the interval where the function $f(x)$ is monotonically decreasing.

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