
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
Let the function $f(x)=\ln x-2ax+2a$, $g(x)=xf(x)+ax^2-x$ ($a\in \mathbb{R}$).

(Ⅰ) Find the monotonic intervals of the function $f(x)$.

(Ⅱ) If the function $g(x)$ attains a maximum value at $x=1$, find the range of values for the positive real number $a$.

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