
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 $F(x) = \int_{0}^{x} (t^{2} + 2t - 8) \, dt$, where $x > 0$.
1. Determine the intervals of monotonicity for $F(x)$.
2. Find the maximum and minimum values of the function $F(x)$ on the interval $[1, 3]$.

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