
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
If the circle $C: (x+1)^{2} + (y-2)^{2} = 2$ is symmetric with respect to the line $2ax + by + 6 = 0$, and a tangent line is drawn from point $P(a,b)$ to circle $C$ with tangent point $A$, then the minimum value of $|PA|$ is ______.

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