
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
On the lateral sides \( KL \) and \( MN \) of the isosceles trapezoid \( KLMN \), points \( P \) and \( Q \) are chosen respectively so that the segment \( PQ \) is parallel to the bases of the trapezoid. It is known that circles can be inscribed in each of the trapezoids \( KPQN \) and \( PLMQ \), and the radii of these circles are equal to \( R \) and \( r \) respectively. Determine the lengths of the bases \( |LM| \) and \( |KN| \).

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