
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
Josef and Marie discovered a regular pyramid while on vacation, the base of which was a square with a side length of $230 \mathrm{~m}$, and its height was equal to the radius of a circle with the same circumference as the base square. Marie labeled the vertices of the square as $A B C D$. Josef marked a point $E$ on the line connecting point $B$ with the apex of the pyramid such that the length of the broken line $A E C$ was the shortest possible.

Determine the length of the broken line $A E C$ rounded to whole centimeters.

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