
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 $f(x)=\frac{1}{2}x^{2}-(2a+2)x+(2a+1)\ln x$, if the slope of the tangent line to the curve $y=f(x)$ at the point $(2,f(2))$ is less than zero,
(1) Find the interval where the function $f(x)$ is increasing;
(2) For any $x_{1}$, $x_{2}\in[0,2]$ ($x_{1}\neq x_{2}$), and $a\in[\frac{3}{2}, \frac{5}{2}]$, the inequality $|f(x_{1})-f(x_{2})| < λ|\frac{1}{x_{1}}-\frac{1}{x_{2}}|$ holds. Find the range of values for the real number $λ$.

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