
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 \( f(x)=a \sin x-\frac{1}{2} \cos 2 x+a-\frac{3}{a}+\frac{1}{2} \), where \( a \in \mathbb{R} \) and \( a \neq 0 \):
1. If \( f(x) \leq 0 \) for any \( x \in \mathbb{R} \), find the range of values for \( a \).
2. If \( a \geq 2 \) and there exists \( x \in \mathbb{R} \) such that \( f(x) \leq 0 \), find the range of values for \( a \).

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