
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 that $m$ is a real number, the function $f(x)=\frac{2m}{3}x^{3}+x^{2}-3x-mx+2$ and its derivative $g(x)=f'(x)$.

(1) Find the monotonic intervals of $f(x)$ when $m=1$;
(2) Find the range of $m$ if $g(x)$ has a zero point in the interval $[-1,1]$.

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