
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
In a cyclic quadrilateral \( Z_{1} Z_{2} Z_{3} Z_{4} \), the product of the lengths of the diagonals is equal to the sum of the products of the lengths of opposite sides:
$$
\left|Z_{1}-Z_{3}\right|\left|Z_{2}-Z_{4}\right|=\left|Z_{1}-Z_{2}\right|\left|Z_{3}-Z_{4}\right|+\left|Z_{1}-Z_{4}\right|\left|Z_{2}-Z_{3}\right|.
$$

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