
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 $f(x) = x^2 + 2ax + 3$, where $x \in [-4, 6]$.

1. Find the maximum and minimum values of $f(x)$ when $a = -2$.
2. Find the range of values of $a$ such that $y = f(x)$ is a monotonous function on the interval $[-4, 6]$.
3. Find the minimum value of $f(x) = x^2 + 2ax + 3$ on the interval $[-4, 6]$.

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