
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 planar vectors $\overset{⇀}{a}=\left(m,-1\right)$ and $\overset{⇀}{b}=\left(2,4\right)$, where $\overrightarrow{a}\bot\overrightarrow{b}$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, find the value of $m$ and the magnitude of $\overrightarrow{c}$, denoted as $|\overrightarrow{c}|$.

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