
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 that $z+1$ is the imaginary root of the equation $x^2+mx+n=0$, where $m,n \in \mathbb{R}$ and $i$ is the imaginary unit.
(1) Find the values of $m$ and $n$ when $z=-1+i$.
(2) If $n=1$, in the complex plane, let point $P$ correspond to the complex number $z$, and point $Q$ correspond to the complex number $2+4i$. Find the range of $|PQ|$.

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