
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 $f(x)=x^{2}-2ax+\ln x$.

(1) When $a=1$, find the monotonic intervals of the function $f(x)$:

(2) If $f′(x)$ is the derivative of $f(x)$, and $f(x)$ has two distinct extreme points $x_{1}$, $x_{2}(x_{1} < x_{2})$, find the minimum value of $2f(x_{1})-f(x_{2})$.

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