
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) Given a convex quadrilateral \(ABCD\), let \(r_1 \leq r_2 \leq r_3 \leq r_4\) be the radii of the inscribed circles of triangles \(ABC\), \(BCD\), \(CDA\), and \(DAB\), respectively, taken in increasing order. Can it be that \(r_4 > 2r_3\)?

b) In a convex quadrilateral \(ABCD\), the diagonals intersect at point \(E\). Let \(r_1 \leq r_2 \leq r_3 \leq r_4\) be the radii of the inscribed circles of triangles \(ABE\), \(BCE\), \(CDE\), and \(DAE\), respectively, taken in increasing order. Can it be that \(r_2 > 2r_1\)?

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