
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 $f(x)=x^{3}-ax^{2}-3x$,
(1) Find the range of values for the real number $a$ such that $f(x)$ is an increasing function in the interval $[1,+\infty)$;
(2) If $x=-\frac{1}{3}$ is an extreme point of $f(x)$, find the maximum value of $f(x)$ in the interval $[1,4]$.

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