
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
Consider an isosceles right triangle $DEF$ where $DE = DF = 24$ units. How many distinct line segments with integer length can be drawn from vertex $D$ to a point on the hypotenuse $\overline{EF}$?
- $\textbf{A)}\ 6$
- $\textbf{B)}\ 8$
- $\textbf{C)}\ 10$
- $\textbf{D)}\ 12$
- $\textbf{E)}\ 14$

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