
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 midline is 10 and one of its bases is 8.

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