
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 median of a right triangle is drawn to the hypotenuse. [Right triangle with an angle of \( 30^\circ \)]

The midline of a trapezoid is 5, and the segment connecting the midpoints of the bases is 3. The angles at the larger base of the trapezoid are \( 30^\circ \) and \( 60^\circ \).

Find the bases and the shorter leg of the trapezoid.

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