
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
In right $\Delta DEF$, $\angle DFE$ is a right angle. Point $N$ is the midpoint of $\overline{EF}$. What is the number of centimeters in the length of median $\overline{DN}$? Additionally, calculate the length of the altitude from point $D$ to $\overline{EF}$. The lengths of sides $\overline{DE}$ and $\overline{DF}$ are 6 cm and 8 cm respectively. [asy] pair D,E,F,N;
D = (0,0); E = (8,0); F = (0,6); N = (E+F)/2;
draw(N--D--E--F--D);
label("$D$",D,W); label("$E$",E,E);
label("$F$",F,W); label("$N$",N,NE);
label("6 cm",D--F,W); label("8 cm",D--E,S);
[/asy]

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