
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 $ABCD$ has parallel sides $\overline{AB}$ of length $25$ and $\overline{CD}$ of length $15$. Sides $\overline{AD}$ and $\overline{BC}$ have lengths $9$ and $12$ respectively. The angles $A$ and $B$ are obtuse. Determine the length of the shorter diagonal of $ABCD$.

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