
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 convex quadrilateral’s diagonals are perpendicular to each other. Consider the sum of the diameters of the circles inscribed in the four parts created by these diagonals. How can this sum be expressed in terms of the quadrilateral’s diagonals and perimeter?

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