
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
The area of triangle $\triangle ABC$ is 10 cm². What is the minimum value in centimeters that the circumference of the circumscribed circle around triangle $\triangle ABC$ can take, given that the midpoints of the altitudes of this triangle lie on one straight line? If the answer is not an integer, round it to the nearest whole number.

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