
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 center of a circle inscribed in a quadrilateral lies on one of its diagonals, which is equal to 5. It is known that the perimeter of the quadrilateral is 14 and its area is 12. Find the length of the other diagonal and the sides of the quadrilateral.

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