
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
Given \( m = \frac{\sin x}{\sin (y-z)}, n = \frac{\sin y}{\sin (z-x)}, p = \frac{\sin z}{\sin (x-y)} \), find the value of \( m n + n p + p m \).

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