
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 a circle $C: x^{2}+y^{2}=16$ and a line $l: (a-b)x + (3b-2a)y - a = 0$ where $a$ and $b$ are not both zero. As $a$ and $b$ vary, the minimum value of the chord length intercepted by the circle $C$ and the line $l$ is ____.

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