
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 $f(x)=2x^{3}+3mx^{2}+3nx-6$, it takes extreme values at $x=1$ and $x=2$.

1. Find the values of $m$ and $n$.
2. Find the monotonic intervals of $f(x)$.

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