Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Let $F_1 = \left( -3, 1 - \frac{\sqrt{5}}{4} \right)$ and $F_ 2= \left( -3, 1 + \frac{\sqrt{5}}{4} \right).$  Then the set of points $P$ such that
\[|PF_1 - PF_2| = 1\]form a hyperbola.  The equation of this hyperbola can be written as
\[\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1,\]where $a, b > 0.$ Find $h + k + a + b.$
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