
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
(12 points) Given the quadratic function $y=x^2+2ax+3$, where $x \in R$:
1. If $a = -1$, write down the intervals of increase and decrease for the function.
2. If $a = -2$, find the maximum and minimum values of the function.
3. If the function is monotonic on $R$, determine the range of real values for $a$.

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