
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
A hyperbola has its center at $(3, -1)$, one focus at $(3 + \sqrt{45}, -1)$, and one vertex at $(6, -1)$. The equation of this hyperbola can be written as 
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]
Find $h + k + a + b.$

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