
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 that the value of the function \( f(x) = \frac{1}{(x-2)^{2}} - 2x + \cos 2\theta - 3 \sin \theta + 2 \) is always positive for \( x \in (-\infty, 2) \), determine the range of the parameter \( \theta \) within the interval \( (0, \pi) \).

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