
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 $f(x)=mx^{2}+(m+4)x+3$.
(1) Determine the value of $m$ such that $f(x)$ has two roots, and the absolute difference between these two roots is minimized. Also, find this minimum value.
(2) If $m=-1$, find the range of $a$ such that there exists an $x$ in $[0,λ]$ (where $λ$ is a positive number) that makes $f(x)-a > 0$.

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