
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 \( f(x) = \ln x - a \cdot \sin(x-1) \), where \( a \in \mathbb{R} \):
- (I) If the slope of the tangent line to the curve \( y=f(x) \) at \( x=1 \) is \( -1 \), find the value of \( a \);
- (II) If \( f(x) \) is an increasing function on the interval \( (0,1) \), determine the range of possible values for \( a \).

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