
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
In a specific hyperbola, the center is at \((1, -1)\), one focus is at \((1, 5)\), and one vertex is at \((1, 2)\). The equation of the hyperbola can be written as 
\[
\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1.
\]
Find \(h + k + a + b.\)

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