
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 the diagram, $EFGH$ is a rectangle with sides $EF = 8$ and $EH = 4$, and $JKLM$ is another rectangle with $KL = 12$ and $JM = 4$. The sides $EH$ and $JK$ are perpendicular. If the shaded area (intersection of $EFGH$ and $JKLM$) is equal to a third of the area of $JKLM$, what is the length of $EM$?

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