
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
Quadrilateral \(ABCD\) is inscribed in a circle, and the areas of triangles \(ABC\) and \(ACD\) are equal. Three sides of the quadrilateral are 4, 6, and 8. Find all possible values for the length of the fourth side.

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