
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
Inside an angle of \(30^\circ\) with vertex \(A\), a point \(K\) is chosen such that its distances to the sides of the angle are 1 and 2. Through point \(K\), all possible lines intersecting the sides of the angle are drawn. Find the minimum perimeter of the triangle formed by the line and the sides of the angle.

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