
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 $f(x)=|x+1|+|2x-1|$ have a minimum value of $a$.  
$(1)$ Find the value of $a$;  
$(2)$ Given $m$, $n > 0$, and $m+n=a$, find the minimum value of $\dfrac {1}{m}+ \dfrac {4}{n}$.

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