
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 $f(x) = 3x^4 - 4(a+1)x^3 + 6ax^2 - 12$ ($a > 0$),
1. Find the intervals of monotonic increase for the function $f(x)$.
2. When $a=2$, find the maximum value of the function $f(x)$.

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