
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 \( r, s \), and \( t \) are nonzero real numbers such that the polynomial \( x^{2} + r x + s \) has \( s \) and \( t \) as roots, and the polynomial \( x^{2} + t x + r \) has 5 as a root. Compute \( s \).

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