
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 three lines \( e_{1}, e_{2}, e_{3} \). We seek the circles \( k_{1}, k_{2}, k_{3} \) such that \( k_{1} \) is tangent to the lines \( e_{2}, e_{3} \) and the circles \( k_{2}, k_{3} \); \( k_{2} \) is tangent to the lines \( e_{3}, e_{1} \) and the circle \( k_{3} \); \( k_{3} \) is tangent to the lines \( e_{1}, e_{2} \). Construct the circles for the following cases:

a) the three lines are parallel;
b) \( e_{3} \) is perpendicular to both \( e_{1} \) and \( e_{2} \).

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