
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 functions $f(x)=x^{3}-9x$ and $g(x)=3x^{2}+a$.
(I) The line $l$ is the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$, and $l$ is also tangent to the curve $y=g(x)$. Find the value of $a$.
(II) If the equation $f(x)=g(x)$ has three distinct real solutions, find the range of real values for $a$.

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