
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 $\overset{⇀}{m}=(2,1)$, $\overset{⇀}{n}=(\sin θ,\cos θ)$, where $θ∈(0, \dfrac{π}{2})$ is the inclination angle of line $l$ passing through point $A(1,4)$, if $\overset{⇀}{m}· \overset{⇀}{n}$ is at its maximum when line $l$ is tangent to the circle $(x+1)^{2}+(y-2)^{2}={r}^{2}(r > 0)$, then $r=$    .

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