
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 of $x$ where $f(x)$ is monotonically increasing;
(2) For any $x_1, x_2 \in [0,2]$ ($x_1 \neq x_2$) and $a \in \left[\frac{3}{2}, \frac {5}{2}\right]$, it always holds that $|f(x_{1})-f(x_{2})| < \lambda \left| \frac {1}{x_{1}}- \frac {1}{x_{2}}\right|$, find the range of the real number $\lambda$.

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