
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 $f(x)=\ln x-ax$ has its tangent line $l$ at $x=2$ parallel to the line $x+2y-3=0$.  
$(1)$ Find the value of the real number $a$;  
$(2)$ If the equation $f(x)+m=2x-x^{2}$ has exactly two distinct real roots in the interval $\left[ \frac {1}{2},2\right]$, find the range of the real number $m$.

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