
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 $F(x)=|2x+t|+x^{2}+x+1 (x\in R, t\in R, t$ is a constant$)$
(I) If $t=-1$, find the extreme value of $F(x)$;
(II) Find the monotonic intervals of $F(x)$ on $R$.

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