
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
Find the maximum and minimum values of each of the following functions:
1) \( u = x^3 - 3x^2 - 9x + 35 \) on the interval \([-4, 4]\);
2) \( p = x^2 \ln x \) on the interval \([1, e]\);
3) \( r = 2 \sin x + \sin 2 x \) on the interval \(\left[0, \frac{3}{2}\right]\);
4) \( y = \arctan(x^2) \).

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