
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 \(\xi\) and \(\eta\) be independent random variables with \(\eta \neq 0\). Express the probabilities \(\mathrm{P}\{\xi \eta \leq z\}\) and \(\mathrm{P}\left\{\frac{\xi}{\eta} \leq z\right\}\) in terms of the functions \(F_{\xi}(x)\) and \(F_{\eta}(y)\).

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