
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 $f(x)=\frac{1}{3}x^{3}-\frac{3}{2}x^{2}+2x+a$,
(1) Find the equation of the tangent line to the graph of $y=f(x)$ at the point $(3,f(3))$ when $a=-\frac{3}{2}$;
(2) If the equation $f(x)=0$ has three distinct real roots, find the range of values for the real number $a$.

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