
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
The circles \( k_{1} \) and \( k_{2} \) have two common tangents \( e \) and \( f \). The tangents parallel to \( e \) are \( e_{1} \) and \( e_{2} \), while the tangents parallel to \( f \) are \( f_{1} \) and \( f_{2} \). Under what condition and how can the circles be reconstructed from the lines \( e_{1}, e_{2}, f_{1}, \) and \( f_{2} \)?

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