
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
If $a, b, c, d$ are the side lengths of a convex quadrilateral $A B C D$ in sequence, and $m$ and $n$ are the lengths of its diagonals, then $m^{2} n^{2} = a^{2} c^{2} + b^{2} d^{2} - 2 a b c d \cos (A+C)$.

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