
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 $f(x)=\ln x-ax$, $(a\in R)$, $g(x)=-x^{2}+2x+1$.
(I) Find the monotonic intervals of $f(x)$;
(II) If for any $x_{1}\in[1,e]$, there always exists $x_{2}\in[0,3]$ such that $f(x_{1})=g(x_{2})$, find the range of values for the real number $a$.

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