
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 $a\in R$, let $f\left(x\right)=\left|{x}^{2}+ax\right|$.

(I) Find the range of values for $a$ such that $f\left(x\right)$ is monotonically increasing on $\left[0,1\right]$;

(II) Denote $M\left(a\right)$ as the maximum value of $f\left(x\right)$ on $\left[0,1\right]$, and find the minimum value of $M\left(a\right)$.

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