
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 the line $l$ passes through point P$(-2, 0)$ and intersects with circle C: $x^2 + y^2 - 4x - 2y + 1 = 0$ at two points A and B, and that $8\overrightarrow{PA} = 5\overrightarrow{AB}$, find the length of $|AB|$.

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