
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 $f(x)=x^{3}-ax^{2}+10$.
(1) When $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(2,f(2))$;
(2) There exists a real number $x$ in the interval $[1,2]$ such that $f(x) < 0$, find the range of values for the real number $a$.

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