
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
Point \(P(x,y)\) is a moving point on line \(2x+y+4=0\). \(PA\) and \(PB\) are two tangents to the circle \(x^{2}+(y-1)^{2}=1\), with \(A\) and \(B\) being the points of tangency. Find the minimum perimeter of triangle \(PAB\).

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