
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
Rectangle $JKLM$ has sides $\overline{JK}$ of length 5 and $\overline{LM}$ of length 12. Divide $\overline{JK}$ into 200 congruent segments with points $J=P_0, P_1, \ldots, P_{200}=K$, and divide $\overline{LM}$ into 200 congruent segments with points $L=Q_0, Q_1, \ldots, Q_{200}=M$. For $1 \le k \le 199$, draw the segments $\overline{P_kQ_k}$. Repeat this construction on the sides $\overline{JL}$ and $\overline{KM}$, and then draw the diagonal $\overline{JM}$. Determine the sum of the lengths of the 399 parallel segments drawn.

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