
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

Two circles \( S_{1} \) and \( S_{2} \), and a line \( l \) are given. Draw a line \( l_{1} \), parallel to the line \( l \), such that:

a) The distance between the points of intersection of \( l_{1} \) with the circles \( S_{1} \) and \( S_{2} \) has a given value \( a \);

b) \( S_{1} \) and \( S_{2} \) cut equal chords on \( l_{1} \);

c) \( S_{1} \) and \( S_{2} \) cut chords on \( l_{1} \) whose sum (or difference) has a given value \( a \).

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