
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 $\triangle DEF$, $DE = 14, EF = 15,$ and $FD = 13$. Also, $N$ is the midpoint of side $DE$ and $J$ is the foot of the altitude from $D$ to $EF$. Determine the length of $JN$.
A) 9.5
B) 10.5
C) 11.2
D) 12.0

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