
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 quadratic function $y=x^{2}+2ax+3$, $x\in \left[-4,6\right]$.  
$(1)$ If $a=-1$, write down the intervals where the function is increasing and decreasing.  
$(2)$ If the function is monotonically increasing on $\left[-4,6\right]$, find the range of real numbers for $a$.

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