
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 $f(x)=|ax^{2}-1|+x$, where $a\in R$.
(I) If $a=2$, and the inequality $f(x)-m\leqslant 0$ has a solution in $R$, find the minimum value of $m$;
(II) If the function $f(x)$ is not monotonic in the interval $[-3,2]$, find the range of $a$.

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