
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
Let the function $f(x)=|x-a|+|2x+4|-3$ $(a\neq -2)$.  
$(1)$ Compare the size of $f(a)$ and $f(-2)$.  
$(2)$ If the graph of the function $f(x)$ can form a triangle with the $x$-axis, find the range of the real number $a$.

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