
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
Points \( M \) and \( K \) are located on the lateral side \( A B \), while points \( N \) and \( L \) are located on the lateral side \( C D \) of trapezoid \( A B C D \), with \( M N \parallel A D \). It is known that the areas of trapezoids \( M B C N \) and \( M A D N \) are in the ratio \( 1:5 \). Find \( M N \) and \( K L \), if \( B C = a \) and \( A D = b \).

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