
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 paper right triangle is folded along a line so that the vertex of the right angle coincides with the other vertex.

a) In what ratio are the diagonals of the resulting quadrilateral divided by their point of intersection?

b) The resulting quadrilateral is cut along the diagonal extending from the third vertex of the original triangle. Find the area of the smallest piece of paper formed.

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