
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 $f(x)=-|x|-|x+2|$.
$(1)$ Solve the inequality $f(x) < -4$;
$(2)$ If the positive real numbers $a$ and $b$ satisfy $a+b= \sqrt {5}$, compare the size of $a^{2}+ \frac {b^{2}}{4}$ and $f(x)+3$, and explain the reason.

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