
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
Mary is attempting to solve the quadratic equation by completing the square: 
$$x^2 - 10x + 15 = 0.$$
She manages to rewrite this equation in the form:
$$(x + b)^2 = c,$$
where $b$ and $c$ are integers. What are the values of $b + c$?

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