
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 \( P \) be the parabola with equation \( y = x^2 + 5 \) and let \( Q = (10, 10) \). There are real numbers \( r \) and \( s \) such that the line through \( Q \) with slope \( m \) does not intersect \( P \) if and only if \( r < m < s \). What is \( r + s \)?

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