
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
A regular quadrangular pyramid has a base $ABCD$, a vertex $E$, and a center of the base $O$. The length of a lateral edge is twice the length of a base edge. Where is the point $M$ on the $EO$ segment such that the sum of the areas of the triangles $MAE$ and $MAB$ is minimized?

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