
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 line \(L\) contains the distinct points \(A\), \(B\), \(C\), \(D\) in that order. Construct a rectangle whose sides (or their extensions) intersect \(L\) at \(A\), \(B\), \(C\), and \(D\) such that the side which intersects \(L\) at \(C\) has length \(k\). How many such rectangles are there?

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