
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
(1) Find the range of the function $y = \frac{12\sqrt{x+1}}{3x+4}$;
(2) Find the minimum value of the function $y = \frac{x^2 + 3x + 3}{x+1}, x \in (-1, +\infty)$;
(3) Find the minimum value of the function $y = \frac{(x^2+1)^2}{(3x^2+2)(2x^2+3)}, x \in (0, +\infty)$;
(4) Find the maximum value of the function $y = \sin x \cos^2 x, x \in \left(0, \frac{\pi}{2}\right)$.

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