
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
Given the quadratic equation $x^2 - 5x + k = 0$ where $r$ and $s$ are the roots, create a new quadratic equation $x^2 + ax + b = 0$ such that the roots of this new equation are $r^2 + 1$ and $s^2 + 1$, find the value of $a$ given that $k = 6$.

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