
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
$ABCDEF$ is a regular hexagon with a mirrored inner surface. A light ray originates from point $A$ and, after two reflections off the sides of the hexagon (at points $M$ and $N$), reaches point $D$. Find the tangent of angle $EAM$.

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