
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 $f(x)=bx^{3}- \frac {3}{2}(2b+1)x^{2}+6x+a$ ($b > 0$).  
$(1)$ Find the intervals of monotonicity for $f(x)$;  
$(2)$ Let $b=1$, if the equation $f(x)=0$ has exactly one real root, find the range of values for $a$.

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