
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 that the graph of the function $f(x)$ is symmetric to the graph of the function $h(x)=x+ \frac {1}{x}+2$ about the point $A(0,1)$.
$(1)$ Find the analytical expression of $f(x)$;
$(2)$ If $g(x)=f(x)+ \frac {a}{x}$, and $g(x)$ is a decreasing function on the interval $(0,2]$, find the range of the real number $a$.

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