
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
Let \( a = \sqrt{17} \) and \( b = i \sqrt{19} \), where \( i = \sqrt{-1} \). Find the maximum possible value of the ratio \( \frac{|a - z|}{|b - z|} \) over all complex numbers \( z \) of magnitude 1 (i.e., over the unit circle \( |z| = 1 \)).

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