
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
Given right triangle $DEF$ has leg lengths $DE=24$ and $EF=25$. Including $\overline{DE}$ and $\overline{EF}$, find the number of line segments with integer length that can be drawn from vertex $E$ to a point on hypotenuse $\overline{DF}$.

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