
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
Let real numbers \( s \) and \( t \) satisfy \( 19s^2 + 99s + 1 = 0 \) and \( t^2 + 99t + 19 = 0 \), respectively, with \( st \neq 1 \). Find the value of \(\frac{st + 4s + 1}{t}\).

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