
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
Suppose there exist nonzero complex numbers \( p, q, r, \) and \( s \) such that \( m \) is a root of both the equations \( px^2 + qx + r = 0 \) and \( qx^2 + rx + s = 0. \) Enter all possible values of \( m, \) separated by commas.

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