
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
A right triangle has one angle measuring $30^\circ$. This triangle shares its hypotenuse with a second triangle that is also right-angled. The two triangles together form a quadrilateral. If the other acute angle in the second triangle is $45^\circ$, find the area of the quadrilateral given that the hypotenuse common to both triangles is 10 units long.

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