
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
We have two rectangles, where rectangle $ABCD$ has sides $\overline {AB}$ of length 5 and $\overline {CB}$ of length 6. Rectangle $EFGH$ surrounds rectangle $ABCD$, sharing the side $AB$ ($E$ coincides with $A$ and $F$ with $B$), with side $\overline {EF}$ having a length of 5 and $\overline {FG}$ being 8. Divide $\overline {AB}$ (also $\overline {EF}$) into 200 congruent segments and $\overline {CB}$ into 200 congruent segments with points respectively. Draw lines connecting these divisions paralleling the sides of each rectangle. Repeat this process for sides $\overline {AH}$ and $\overline {CD}$, considering the segments on $AH$ equal to those on $EF$. Calculate the sum of the lengths of all these segments across both rectangles, excluding the sides of the rectangles.

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