
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
One of the angles of a trapezoid is \(30^\circ\), and the lines containing the lateral sides of the trapezoid intersect at a right angle. Find the length of the shorter lateral side of the trapezoid if its midsegment is 10 cm and one of its bases is 8 cm.

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