
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 $f(x)=|x-m|+|x-n|$.  
$(1)$ If $m=2$, $n=-5$, solve the inequality $f(x) > 9$;  
$(2)$ If $m=a$, $n=- \frac {1}{a}$, where $a\neq 0$, find the minimum value of the function $f(x)$.

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