
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 the line $l: mx - y + 1 - m = 0, m \in R$. If line $l$ passes through the focus of the parabola $y^{2} = 8x$, then $m =$ ; at this time, the length of the chord $ \left| AB \right| =$ intercepted by line $l$ on the circle $({x-1})^{2} + (y-1)^{2} = 6$.

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