
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 \( f(x) \) on \( \mathbb{R} \) satisfies \( f(x) + f(-x) = 0 \), and for \( x > 0 \), \( f(x) = \frac{1}{2}(|x + \sin \alpha| + |x + 2 \sin \alpha|) + \frac{3}{2} \sin \alpha \). If for any \( x \in \mathbb{R} \), \( f(x - 3 \sqrt{3}) \leq f(x) \) always holds, then the range of \( \alpha \) is ______.

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