
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 $f(x)={x}^{3}+a{x}^{2}+bx+c$, it reaches an extreme value at $x=-2$, and its graph is tangent to the line $y=-3x+3$ at the point $(1,0)$.

(1) Find the analytical expression of $f(x)$;
(2) Find the monotonic intervals of $f(x)$.

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