
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
Adva van egy gömb \((O, r)\), egy \((g)\) egyenes és két távolság \((a, b)\). Szerkesszünk olyan \((e)\) egyenest, amely az első képsíkkal párhuzamos és \(g\)-t \(X\)-ben, a gömböt pedig \(Y, Z\)-ben metszi úgy, hogy \(\overline{X Y}=a\) és \(\overline{Y Z}=b\) legyen.

### Translation
Consider a sphere \((O, r)\), a line \((g)\), and two distances \((a, b)\). Construct a line \((e)\) that is parallel to the first principal plane, intersects \(g\) at \(X\), and intersects the sphere at \(Y\) and \(Z\) such that \(\overline{X Y}=a\) and \(\overline{Y Z}=b\).

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