
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
Trapezoid $JKLM$ has parallel sides $\overline{JK}$ of length $40$ and $\overline{LM}$ of length $24$. The other two sides are of lengths $13$ and $15$. The angles $J$ and $K$ are acute. What is the length of the shorter diagonal of $JKLM$?
A) $\frac{25}{4}\sqrt{\frac{2079}{16}}$
B) $\sqrt{\left(\frac{25}{4} + 24\right)^2 + \frac{2079}{16}}$
C) $\sqrt{\left(16 - \frac{25}{4}\right)^2 + \frac{2079}{16}}$
D) $\frac{25}{6}\sqrt{\frac{2704}{16}}$

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