
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
Three of the roots of the equation  $x^4 -px^3 +qx^2 -rx+s = 0$  are  $\tan A, \tan B$ , and  $\tan C$ , where  $A, B$ , and  $C$  are angles of a triangle. Determine the fourth root as a function only of  $p, q, r$ , and  $s.$ 

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