
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 $f(x)= \frac {x^{2}}{2}-4ax+alnx+3a^{2}+2a (a>0)$.
(1) Discuss the monotonicity of $f(x)$;
(2) If $f(x)$ has two extreme points $x_1$, $x_2$, find the maximum value of $f(x_1) + f(x_2)$ as $a$ varies.

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