
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 a regular hexagon $ABCDEF$ of side length $2$, there are two congruent rectangles, $JKLM$ and $NOPQ$, inside the hexagon such that $J, K$ are on $AB$, $L, M$ are on $AF$, and $N, O$ on $CD$, $P, Q$ on $EF$. Find the length of segment $JM$.
A) $\sqrt{2}$ 
B) $2$ 
C) $4$ 
D) $2 - \sqrt{3}$

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