
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. Given that $x < -2$, find the maximum value of the function $y=2x+ \frac{1}{x+2}$.
2. Find the minimum value of the function $y= \frac{x^{2}+5}{ \sqrt{x^{2}+4}}$.
3. If positive numbers $a$ and $b$ satisfy $ab=a+b+3$, find the range of values for $a+b$.

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