
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 $f(x)=x-\frac{a}{x}-(a+1)\ln x (a\in R)$.
(I) Find the monotonic intervals of the function $f(x)$ when $0 < a \leqslant 1$.
(II) Determine whether there exists a real number $a$ such that $f(x) \leqslant x$ always holds. If it exists, find the range of $a$; if not, explain the reason.

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