
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
Assuming that the roots of  $x^3 + p \cdot x^2 + q \cdot x + r = 0$  are real and positive, find a relation between  $p,q$  and  $r$  which gives a necessary condition for the roots to be exactly the cosines of the three angles of a triangle.

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