
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 vectors $\overrightarrow{a}=(m,2)$ and $\overrightarrow{b}=(-1,n)$ with $n > 0$ and $\overrightarrow{a} \cdot \overrightarrow{b} = 0$, and point $P(m,n)$ lies on the circle $x^2 + y^2 = 5$, find the value of $|2\overrightarrow{a} + \overrightarrow{b}|$.

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