
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 $F(x)=\int \_{-1}^{x} t(t-4)dt$, $x\in(-1,+\infty)$.

(1) Find the monotonic intervals of $F(x)$;

(2) Find the maximum and minimum values of the function $F(x)$ on $[1,5]$.

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