
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 diagonal $KM$ of trapezoid $KLMN$ is 3 times the length of segment $KP$ on this diagonal. The base $KN$ of the trapezoid is 3 times the length of the base $LM$. Find the ratio of the area of trapezoid $KLMN$ to the area of triangle $KPR$, where $R$ is the point of intersection of line $PN$ and side $KL$.

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