
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
Consider the function $f(x)=x^{3}+ax^{2}-9x-1$ where $a < 0$. If the tangent line to the curve $y=f(x)$ with the minimum slope is parallel to the line $12x+y-6=0$,  
(1) Find the value of the real number $a$;  
(2) Find the intervals where the function is monotonically decreasing.

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