
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 $f(x)=\sin x-ax$.  
(I) For $x\in(0,1)$, $f'(x) > 0$ always holds, find the range of the real number $a$;  
(II) When $a=1$, let $h(x)=f(x)-\sin x+\ln x+1$, find the maximum value of $h(x)$.

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